NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.3

NCERT Solutions for Class 12th Maths Chapter 10 Vector Algebra Ex 10.3

Get Free NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.3 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Vector Algebra Exercise 10.3 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 10 Class 12 Vector Algebra Ex 10.3 provided in NCERT Textbook.

Free download NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.3 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.3

Ex 10.3 Class 12 Maths Question 1.
Find the angle between two vectors Image may be NSFW.
Clik here to view. $\overrightarrow { a } ,\overrightarrow { b }$ with magnitudes √3 and 2 respectively, and such that Image may be NSFW.
Clik here to view. $\overrightarrow { a } \cdot \overrightarrow { b } =\sqrt { 6 }$
Solution:
Angle θ between two vectors Image may be NSFW.
Clik here to view. $\overrightarrow { a } ,\overrightarrow { b }$ ,
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 1

Ex 10.3 Class 12 Maths Question 2.
Find the angle between the vectors Image may be NSFW.
Clik here to view. $\hat { i } -2\hat { j } +3\hat { k } \quad and\quad 3\hat { i } -2\hat { j } +\hat { k }$
Solution:
Let Image may be NSFW.
Clik here to view. $\overrightarrow { a } =\hat { i } -2\hat { j } +3\hat { k } \quad and\quad \overrightarrow { b } =3\hat { i } -2\hat { j } +\hat { k }$
Let θ be the angle between Image may be NSFW.
Clik here to view. $\overrightarrow { a } ,\overrightarrow { b }$ ,
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 2

Ex 10.3 Class 12 Maths Question 3.
Find the projection of the vector Image may be NSFW.
Clik here to view. $\overrightarrow { i } -\overrightarrow { j }$ , on the line represented by the vector Image may be NSFW.
Clik here to view. $\overrightarrow { i } +\overrightarrow { j }$ ,
Solution:
let Image may be NSFW.
Clik here to view. $\overrightarrow { a } =\hat { i } -\hat { j } \quad and\quad \overrightarrow { b } =\hat { i } +\hat { j }$
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 3

Ex 10.3 Class 12 Maths Question 4.
Find the projection of the vector Image may be NSFW.
Clik here to view. $\hat { i } +3\hat { j } +7\hat { k }$ on the vector Image may be NSFW.
Clik here to view. $7\hat { i } -\hat { j } +8\hat { k }$
Solution:
let Image may be NSFW.
Clik here to view. $\overrightarrow { a } =\hat { i } +3\hat { j } +7\hat { k } \quad and\quad \overrightarrow { b } =7\hat { i } -\hat { j } +8\hat { k }$ then
Image may be NSFW.
Clik here to view. tiwari academy class 12 maths Chapter 10 Vector Algebra 4

Ex 10.3 Class 12 Maths Question 5.
Show that each of the given three vectors is a unit vector Image may be NSFW.
Clik here to view. $\frac { 1 }{ 7 } \left( 2\hat { i } +3\hat { j } +6\hat { k } \right) ,\frac { 1 }{ 7 } \left( 3\hat { i } -6\hat { j } +2\hat { k } \right) ,\frac { 1 }{ 7 } \left( 6\hat { i } +2\hat { j } -3\hat { k } \right)$ Also show that they are mutually perpendicular to each other.
Solution:
Image may be NSFW.
Clik here to view. $Let\quad \overrightarrow { a } =\frac { 1 }{ 7 } \left( 2\hat { i } +3\hat { j } +6\hat { k } \right) ,\overrightarrow { b } =\frac { 1 }{ 7 } \left( 3\hat { i } -6\hat { j } +2\hat { k } \right) ,\overrightarrow { c } =\frac { 1 }{ 7 } \left( 6\hat { i } +2\hat { j } -3\hat { k } \right)$
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 5

Ex 10.3 Class 12 Maths Question 6.
Image may be NSFW.
Clik here to view. $Find\left| \overrightarrow { a } \right| and\left| \overrightarrow { b } \right| if\left( \overrightarrow { a } +\overrightarrow { b } \right) \cdot \left( \overrightarrow { a } -\overrightarrow { b } \right) =8\quad and\left| \overrightarrow { a } \right| =8\left| \overrightarrow { b } \right|$
Solution:
Given Image may be NSFW.
Clik here to view. $\left( \overrightarrow { a } +\overrightarrow { b } \right) \cdot \left( \overrightarrow { a } -\overrightarrow { b } \right) =8$
Image may be NSFW.
Clik here to view. tiwari academy class 12 maths Chapter 10 Vector Algebra 6

Ex 10.3 Class 12 Maths Question 7.
Evaluate the product :
Image may be NSFW.
Clik here to view. $\left( 3\overrightarrow { a } -5\overrightarrow { b } \right) \cdot \left( 2\overrightarrow { a } +7\overrightarrow { b } \right)$
Solution:
Image may be NSFW.
Clik here to view. $\left( 3\overrightarrow { a } -5\overrightarrow { b } \right) \cdot \left( 2\overrightarrow { a } +7\overrightarrow { b } \right)$
Image may be NSFW.
Clik here to view. $=6\overrightarrow { a } .\overrightarrow { a } -10\overrightarrow { b } \overrightarrow { a } +21\overrightarrow { a } .\overrightarrow { b } -35\overrightarrow { b } .\overrightarrow { b }$
Image may be NSFW.
Clik here to view. $=6{ \left| \overrightarrow { a } \right| }^{ 2 }-11\overrightarrow { a } \overrightarrow { b } -35{ \left| \overrightarrow { b } \right| }^{ 2 }$

Ex 10.3 Class 12 Maths Question 8.
Find the magnitude of two vectors Image may be NSFW.
Clik here to view. $\overrightarrow { a } ,\overrightarrow { b }$ having the same magnitude and such that the angle between them is 60° and their scalar product is Image may be NSFW.
Clik here to view. $\frac { 1 }{ 2 }$
Solution:
We know that Image may be NSFW.
Clik here to view. $\overrightarrow { a } .\overrightarrow { b } =\left| \overrightarrow { a } \right| \left| \overrightarrow { b } \right| cos\theta$
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 8

Ex 10.3 Class 12 Maths Question 9.
Find Image may be NSFW.
Clik here to view. $\left| \overrightarrow { x } \right|$ , if for a unit vector Image may be NSFW.
Clik here to view. $\overrightarrow { a } ,(\overrightarrow { x } -\overrightarrow { a } )\cdot (\overrightarrow { x } +\overrightarrow { a } )=12$
Solution:
Given
Image may be NSFW.
Clik here to view. $\overrightarrow { a } ,(\overrightarrow { x } -\overrightarrow { a } )\cdot (\overrightarrow { x } +\overrightarrow { a } )=12$
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 9

Ex 10.3 Class 12 Maths Question 10.
If Image may be NSFW.
Clik here to view. $\overrightarrow { a } =2\hat { i } +2\hat { j } +3\hat { k } ,\overrightarrow { b } =-\hat { i } +2\hat { j } +\hat { k } and\overrightarrow { c } =3\hat { i } +\hat { j }$ such that Image may be NSFW.
Clik here to view. $\overrightarrow { a } +\lambda \overrightarrow { b } \bot \overrightarrow { c }$ , then find the value of λ.
Solution:
Given
Image may be NSFW.
Clik here to view. $\overrightarrow { a } =2\hat { i } +2\hat { j } +3\hat { k } ,\overrightarrow { b } =-\hat { i } +2\hat { j } +\hat { k } and\overrightarrow { c } =3\hat { i } +\hat { j }$
Image may be NSFW.
Clik here to view. tiwari academy class 12 maths Chapter 10 Vector Algebra 10

Ex 10.3 Class 12 Maths Question 11.
Show that Image may be NSFW.
Clik here to view. $\left| \overrightarrow { a } \right| \overrightarrow { b } +\left| \overrightarrow { b } \right| a\quad \bot \quad \left| \overrightarrow { a } \right| \cdot \overrightarrow { b } -\left| \overrightarrow { b } \right| a$ for any two non-zero vectors Image may be NSFW.
Clik here to view. $\overrightarrow { a } ,\overrightarrow { b }$
Solution:
Image may be NSFW.
Clik here to view. $\overrightarrow { a } ,\overrightarrow { b }$ are any two non zero vectors
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 11

Ex 10.3 Class 12 Maths Question 12.
If Image may be NSFW.
Clik here to view. $\overrightarrow { a } \cdot \overrightarrow { a } =0\quad and\quad \overrightarrow { a } \cdot \overrightarrow { b } =0$ , then what can be concluded about the vector Image may be NSFW.
Clik here to view. $\overrightarrow { b }$ ?
Solution:
Image may be NSFW.
Clik here to view. $\overrightarrow { a } \overrightarrow { a } =0\quad and\quad \overrightarrow { a } .\overrightarrow { b } =0$ ,
=> Image may be NSFW.
Clik here to view. $\overrightarrow { b }$ = 0
Hence b is any vector.

Ex 10.3 Class 12 Maths Question 13.
If Image may be NSFW.
Clik here to view. $\overrightarrow { a } ,\overrightarrow { b } ,\overrightarrow { c }$ are the unit vector such that Image may be NSFW.
Clik here to view. $\overrightarrow { a } +\overrightarrow { b } +\overrightarrow { c } =0$ , then find the value of Image may be NSFW.
Clik here to view. $\overrightarrow { a } .\overrightarrow { b } +\overrightarrow { b } .\overrightarrow { c } +\overrightarrow { c } .\overrightarrow { a }$
Solution:
We have
Image may be NSFW.
Clik here to view. $\overrightarrow { a } +\overrightarrow { b } +\overrightarrow { c } =0$
Image may be NSFW.
Clik here to view. tiwari academy class 12 maths Chapter 10 Vector Algebra 13

Ex 10.3 Class 12 Maths Question 14.
If either vector Image may be NSFW.
Clik here to view. $\overrightarrow { a } =0\quad or\quad \overrightarrow { b } =0$ then Image may be NSFW.
Clik here to view. $\overrightarrow { a } .\overrightarrow { b } =0$ . But the converse need not be true. Justify your answer with an example.
Solution:
Given: Image may be NSFW.
Clik here to view. $\overrightarrow { a } =0\quad or\quad \overrightarrow { b } =0$
To prove: Image may be NSFW.
Clik here to view. $\overrightarrow { a } .\overrightarrow { b } =0$
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 14

Ex 10.3 Class 12 Maths Question 15.
If the vertices A,B,C of a triangle ABC are (1,2,3) (-1,0,0), (0,1,2) respectively, then find ∠ABC.
Solution:
Let O be the origin then.
Image may be NSFW.
Clik here to view. $\frac { 1 }{ 2 }$
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 15
Image may be NSFW.
Clik here to view.

Ex 10.3 Class 12 Maths Question 16.
Show that the points A (1,2,7), B (2,6,3) and C (3,10, -1) are collinear.
Solution:
The position vectors of points A, B, C are
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 16

Ex 10.3 Class 12 Maths Question 17.
Show that the vectors Image may be NSFW.
Clik here to view. $2\hat { i } -\hat { j } +\hat { k } ,\hat { i } -3\hat { j } -5\hat { k }$ and Image may be NSFW.
Clik here to view. $\left( 3\hat { i } -4\hat { j } -4\hat { k } \right)$ from the vertices of a right angled triangle.
Solution:
The position vectors of the points A, B and C are
Image may be NSFW.
Clik here to view. $2\hat { i } -\hat { j } +\hat { k } ,\hat { i } -3\hat { j } -5\hat { k }$ and Image may be NSFW.
Clik here to view. $\left( 3\hat { i } -4\hat { j } -4\hat { k } \right)$
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 17
Image may be NSFW.
Clik here to view.

Ex 10.3 Class 12 Maths Question 18.
If Image may be NSFW.
Clik here to view. $\overrightarrow { a }$ is a non-zero vector of magnitude ‘a’ and λ is a non- zero scalar, then λ Image may be NSFW.
Clik here to view. $\overrightarrow { a }$ is unit vector if
(a) λ = 1
(b) λ = – 1
(c) a = |λ|
(d) a = Image may be NSFW.
Clik here to view. $\frac { 1 }{ \left| \lambda \right| }$
Solution:
Image may be NSFW.
Clik here to view. $\left| \overrightarrow { a } \right| =a$
Given : Image may be NSFW.
Clik here to view. $\lambda \overrightarrow { a }$ is a unit vectors
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 18

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Hindi Medium Ex 10.3

Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Exercise 10.3 of Vector Algebra
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view. 12 Maths Exercise 10.3 solutions
Image may be NSFW.
Clik here to view. 12 Maths Exercise 10.3 all answers
Image may be NSFW.
Clik here to view. 12 Maths Exercise 10.3 in English Medium
Image may be NSFW.
Clik here to view. 12 Maths Exercise 10.3 in Hindi Medium
Image may be NSFW.
Clik here to view. Class 12 Maths Exercise 10.3 in Hindi medium
Image may be NSFW.
Clik here to view. Class 12 Maths Exercise 10.3 for 2019-20
Image may be NSFW.
Clik here to view. Class 12 Maths Exercise 10.3 updated