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NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3

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NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3

Get Free NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Determinants Exercise 4.3 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 4 Class 12 Determinants Ex 4.3 provided in NCERT Textbook.

Free download NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3 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.

The topics and sub-topics included in the Determinants chapter are the following:

Section NameTopic Name
4Determinants
4.1Introduction
4.2Determinant
4.3Properties of Determinants
4.4Area of a Triangle
4.5Adjoint and Inverse of a Matrix
4.6Applications of Determinants and Matrices
4.7Summary

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3

Ex 4.3 Class 12 Maths Question 1.
Find the area of the triangle with vertices at the point given in each of the following:
(i) (1,0), (6,0) (4,3)
(ii) (2,7), (1,1), (10,8)
(iii) (-2,-3), (3,2), (-1,-8)
Solution:
(i) Area of triangle = \frac { 1 }{ 2 } \left| \begin{matrix} 1\quad & 0 & \quad 1 \\ 6\quad & 0 & \quad 1 \\ 4\quad & 3 & \quad 1 \end{matrix} \right|
= \\ \frac { 1 }{ 2 } [1(0-3)+1(18-0)]
= 7.5 sq units
NCERT Solutions for Class 12 Maths Chapter 4 Determinants 1

Ex 4.3 Class 12 Maths Question 2.
Show that the points A (a, b + c), B (b, c + a) C (c, a+b) are collinear.
Solution:
The vertices of ∆ABC are A (a, b + c), B (b, c + a) and C (c, a + b)
NCERT Solutions for Class 12 Maths Chapter 4 Determinants 2

Ex 4.3 Class 12 Maths Question 3.
Find the value of k if area of triangle is 4 square units and vertices are
(i) (k, 0), (4,0), (0,2)
(ii) (-2,0), (0,4), (0, k).
Solution:
(i) Area of ∆ = 4 (Given)
\frac { 1 }{ 2 } \left| \begin{matrix} k\quad & 0 & \quad 1 \\ 4\quad & 0 & \quad 1 \\ 0\quad & 2 & \quad 1 \end{matrix} \right|
= \\ \frac { 1 }{ 2 } [-2k+8]
= -k+4
Case (a): -k + 4 = 4 ==> k = 0
Case(b): -k + 4 = -4 ==> k = 8
Hence, k = 0,8
(ii) The area of the triangle whose vertices are (-2,0), (0,4), (0, k)
byjus class 12 maths Chapter 4 Determinants 3

Ex 4.3 Class 12 Maths Question 4.
(i) Find the equation of line joining (1, 2) and (3,6) using determinants.
(ii) Find the equation of line joining (3,1), (9,3) using determinants.
Solution:
(i) Given: Points (1,2), (3,6)
Equation of the line is
NCERT Solutions for Class 12 Maths Chapter 4 Determinants 4

Ex 4.3 Class 12 Maths Question 5.
If area of triangle is 35 sq. units with vertices (2, – 6), (5,4) and (k, 4). Then k is
(a) 12
(b) – 2
(c) -12,-2
(d) 12,-2
Solution:
(d) Area of ∆ = \frac { 1 }{ 2 } \left| \begin{matrix} 2\quad & -6 & \quad 1 \\ 5\quad & 4 & \quad 1 \\ k\quad & 4 & \quad 1 \end{matrix} \right|
= \\ \frac { 1 }{ 2 } [50 – 10k] = 25 – 5k
∴ 25-5k = 35 or 25-5k = -35
-5k = 10 or 5k = 60
=> k = -2 or k = 12

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Hindi Medium Ex 4.3

NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 Determinants
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 Determinants in English medium PDF
Class 12 Maths Chapter 4 Exercise 4.3 Solutions in Hindi Medium PDF
Class 12 Maths Chapter 4 Exercise 4.3 Question 1, 2, 3, 4, 5, 6, 7
Class 12 Maths Chapter 4 Exercise 4.3 ke prashan uttar

More Resources for NCERT Solutions Class 12:

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