NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 Determinants
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 are created by our experts to help students to understand the concepts of the chapter better. Solve these questions to ace your examinations.
Krati Saraswat16 Jan, 2024
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NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 Determinants
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 Determinants is prepared by the academic team of Physics Wallah. We have prepared NCERT Solutions for all exercises of Chapter 4. Given below are the step-by-step solutions of all questions given in NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 Determinants.CBSE Class 12th Toppers List 2024
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 Overview
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 covers these important topics. Students are encouraged to review each topic thoroughly in order to fully understand the concepts taught in the chapter and make optimal use of the provided solutions. These solutions are the outcome of the dedicated effort that the Physics Wallah teachers have been doing to aid students in understanding the ideas covered in this chapter. After going over and rehearsing these responses, the goal is for students to easily score outstanding exam results.NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 PDF
Our team of teachers at Physics Wallah has developed thorough solutions for NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 in order to help students understand and apply chapter concepts. The purpose of these questions is to help students comprehend explanations. You may obtain the NCERT Solutions for Class 12 Maths, Chapter 4 PDF by clicking on this link:NCERT Solutions Class 12 Maths Chapter 4 PDF Download Link
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3
Solve The Following Questions NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 Determinants
Question 1. Find the area of the triangle with vertices at the points 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) The area of the triangle with vertices (1, 0), (6, 0), (4, 3) is given by the relation, =
(ii) The area of the triangle with vertices (2, 7), (1, 1), (10, 8) is given by the relation,
=
(iii) The area of the triangle with vertices (−2, −3), (3, 2), (−1, −8)
=
Question 2. Show that the points A(a,b + c), B(b, c + a), C(c, a+b) are collinear.
Solution :
Therefore, points A, B and C are collinear.
Question
3. Find values of k if area of triangle is 4 sq. units and vertices are:
(i) ( k , 0), (4, 0), (0, 2)
(ii) (−2, 0), (0, 4), (0, k )
Solution : We know that the area of a triangle whose vertices are ( x 1 , y 1 ), ( x 2 , y 2 ), and ( x 3 , y 3 ) is the absolute value of the determinant (Δ), where
When −
k
+ 4 = − 4,
k
= 8.
When −
k
+ 4 = 4,
k
= 0.
Hence,
k
= 0, 8.
(ii) The area of the triangle with vertices (−2, 0), (0, 4), (0,
k
) is given by the relation,
∴
k
− 4 = ± 4
When
k
− 4 = − 4,
k
= 0.
When
k
− 4 = 4,
k
= 8.
Hence,
k
= 0, 8.
Hence, the equation of the line joining the given points is
y
= 2
x
.
(ii) Let P (
x
,
y
) be any point on the line joining points A (3, 1) and
B (9, 3). Then, the points A, B, and P are collinear. Therefore, the area of triangle ABP will be zero.
Hence, the equation of the line joining the given points is
x
− 3
y
= 0.
It is given that the area of the triangle is ±35.
Therefore, we have:
⇒ 25 - 5k = ± 35
⇒ 5(5 - k) = ± 35
⇒ 5 - k = ± 7
When 5 −
k
= −7,
k
= 5 + 7 = 12.
When 5 −
k
= 7,
k
= 5 − 7 = −2.
Hence,
k
= 12, −2.
The correct answer is D.
Therefore, option (D) is correct.
| NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 | NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.2 |
| NCERT Solutions for Class 12 Maths Chapter 2 Miscellaneous Exercise | |
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 FAQs
What topics are covered in Exercise 4.3 on Determinants in Class 12 Maths?
Exercise 4.3 likely covers various topics related to determinants, such as finding the value of determinants using different methods, applying properties of determinants, and solving problems related to determinants.
How do I find the value of a determinant using expansion by minors?
Expansion by minors involves breaking down a determinant into smaller determinants. The process includes selecting a row or column, forming minors, applying the sign pattern, and summing up the products. The exact steps depend on the size of the matrix.
What are the properties of determinants that are important in Exercise 4.3?
Properties of determinants include scalar multiplication property, row and column operations, interchanging rows or columns, and expansion by minors. Understanding these properties is crucial for simplifying and solving determinant problems.
What are some common mistakes to avoid when working on determinants?
Common mistakes include miscalculations during expansion, errors in sign patterns, and not applying properties correctly. Pay attention to details, double-check your work, and seek clarification if you are unsure.
Are there any shortcuts or tricks for calculating determinants quickly?
While there may be certain techniques to simplify calculations, the most effective way to solve determinant problems is to understand and apply the properties systematically. Practice will lead to increased speed and accuracy.
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