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Edited By Kuldeep Maurya | Updated on Jan 25, 2022 07:12 PM IST

The CBSE board students are recommended to use the RD Sharma solutions books for their references. This is due to the high standard answers provided in the book. It makes the students less dependent on the tutors to clear their silly doubts. When it comes to mathematics, there are high chances that students get more doubts while solving it. Significantly, the students who find it hard to cope with the Determinants portions can use the RD Sharma Class 12th exercise 5.3 solution books.

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**Also Read - **RD Sharma Solution for Class 9 to 12 Maths

- Chapter 5 - Determinants Ex 5.1
- Chapter 5 - Determinants Ex 5.2
- Chapter 5 - Determinants Ex 5.4
- Chapter 5 - Determinants Ex 5.5
- Chapter 5 - Determinants Ex MCQ
- Chapter 5 - Determinants Ex FBQ
- Chapter 5 - Determinants Ex VSA

Determinants Excercise: 5.3

Determinants exercise 5.3 question 1 (ii)

Hints: By putting the values of the co-ordinate in the formulaof area, we will calculate the area of the triangle.

Determinants exercise 5.3 question 1 (iii)

Hints: By putting the values of the co-ordinate in the formulaof area, we will calculate the area of the triangle.

Determinants exercise 5.3 question 1 (iv)

Hints: By putting the values of the co-ordinate in the formulaof area, we will calculate the area of the triangle.

Determinants exercise 5.3 question 2 (i)

Answer: Yes, points are collinear.

Hints: First by using the values of vertices find determinant. If value of determinant is zero, then points are collinear.

Hence, points are collinear.

Determinants exercise 5.3 question 2 (ii)

Answer: Yes, points are collinear.

Hints: First by using the values of vertices find determinant. If value of determinant is zero, then points are collinear.

Hence, points are collinear.

Determinants exercise 5.3 question 2 (iii)

Answer: Yes, points are collinear.

Hints: First by using the values of vertices find determinant. If value of determinant is zero, then points are collinear.

Hence, points are collinear.

Determinants exercise 5.3 question 2 (iv)

Hints: First by using the values of vertices find determinant. If value of determinant is zero, then points are collinear.

Hence, points are collinear.

Determinants exercise 5.3 question 3

**Answer: **Proved.**Hints: **First find determinant and the value of a and b, to prove the given equation.

Explanation: Determinant=0

Hence, proved the given equation.

Determinants exercise 5.3 question 4

**Answer:** Yes, points are collinear.**Hints:** Use the values of vertices and find the determinant. If determinant is zero, points will be collinear.**Explanation:**

Let,

Hence, points are collinear

Determinants exercise 5.3 question 6

**Answer:** = -2**Hints:** Using determinant, find area of triangle and find value of .

area of triangle = 35 sq. Units.

Determinants exercise 5.3 question 7

**Hints:** First find the determinant and then area of the triangle. If result found be zero, then given points are collinear.

**Given:** Vertices are (1,4), (2,3) and (-5, -3).

**Explanation:** Vertices are (1,4), (2,3) and (-5, -3).

and determinant is not zero, that is why points are not collinear.

Determinants exercise 5.3 question 8

**Answer:** 46 sq. units**Hints:** To find area of triangle use modulus in the formula of determinant.**Given:** (-3,5), (3, -6) and (7,2).**Explanation:** Vertices are (-3,5), (3, -6) and (7,2).

Determinants exercise 5.3 question 9

**Hints:** If points are collinear then determinant will be zero.

Expanding along row1.

Determinants exercise 5.3 question 10

**Answer:**=3**Hints:** Use vertices in the determinant formula and equate it with zero because if points are collinear then determinant will be zero and then find the value of x.**Given:** (, -2), (5,2) and (8,8) are collinear.**Explanation:** Vertices are (, -2), (5,2) and (8,8)

Determinants exercise 5.3 question 11

**Answer:**=5**Hints:** Use vertices in the determinant formula and equate it with zero because if points are collinear then determinant will be zero and then find the value of .**Given:** (3,-2), (,2) and (8,8).**Explanation:** Vertices are (3,-2), (,2) and (8,8).

Determinants exercise 5.3 question 12 (i)

**Given: **(1,2) and (3,6)**Explanation:** Vertices are (1,2) and (3,6)

Determinants exercise 5.3 question 12 (ii)

**Given: **(3,1) and (9,3)**Explanation:** Vertices are (3,1) and (9,3)

Determinants exercise 5.3 question 13 (i)

**Answer:**=0**Hints:** Putting the values of vertices, in the formula of area of triangle.**Given:** (,0), (4,0) and (0,2)

area of triangle= 4 sq. units**Explanation:** Vertices are (,0), (4,0) and (0,2)

Determinants exercise 5.3 question 13 (ii)

**Answer:**=8**Hints:** Putting the values of vertices, in the formula of area of triangle.**Given:** (-2,0), (0,4) and (0,)

area of triangle= 4 sq. units**Explanation:** Vertices are (-2,0), (0,4) and (0,)

The 5th chapter for Class 12 mathematics, Determinants, is a simple chapter where many students aim to score their best. RD Sharma class 12th exercise 5.3, has around 21 questions to be solved, including its subparts. The concepts in this exercise are Area of the Triangle with vertices at given points, Collinear points, and the Equation of lines using Determinants. All these can be referred to at the RD Sharma Class 12 Chapter 5 Exercise 5.3.

All the solutions in this book are created and verified by the experts according to the latest syllabus. It follows the NCERT pattern too. Hence, the CBSE board students can use it to complete their homework and assignments and prepare for their tests. Scoring better marks in the Determinants chapter will boost up your total score. Therefore, the RD Sharma Chapter 5 Exercise 5.3 Solution will make you understand the concepts effortlessly. Numerous practice questions will make you furthermore clear about exercise 5.3.

You might think that RD Sharma solutions book would cost a lot by looking at its benefits. But that is not the case here. The RD Sharma Class 12 Solutions Determinants Ex 5.3 can be downloaded free from top educational websites like Career 360. RD Sharma Class 12th exercise 5.3 materials are available for free of cost on this website. So, all you need to do is, visit the Career 360 website, look out for the solution book you need and download it to your device. Then, start practicing the sums from day 1 to achieve more marks in your public exam.

Once you commence preparing for your tests using the RD Sharma solutions books, you can witness yourself crossing all your benchmarks. Many students have benefited from the RD Sharma Class 12 Solutions Chapter 5 ex 5.3 to know the concepts of Determinants better. There are high chances that questions in the public exam can be asked from the RD Sharma solution books. Hence, preparing with this material in advance leads you to score better marks in the examinations easily.

**Chapter-wise RD Sharma Class 12 Solutions**

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

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Download E-book1. Where can I find the RD Sharma solution books?

The RD Sharma solution books can be found on the Career360 website. In addition, you can download the PDF file for your reference.

2. Where can I clear my doubts regarding the concept of the determinant?

If you have doubts while solving the sums in the determinants chapter, use the RD Sharma Class 12th exercise 5.3 solution books. A clear explanation of each concept in this book and the answer key for every question are given.

3. Can a slow-learner student understand the concepts in the RD Sharma books?

The solutions in this book are provided in various methods, the elaborated ones, and the shortcut methods. Hence, any category of students can use the RD Sharma solution books as their reference guide.

4. How much does the Class 12 RD Sharma Chapter 5 Exercise 5.3 Solution books cost?

The RD Sharma Class 12th exercise 5.3 solution books can be downloaded for free from the Career360 website. So, you do not pay even a single penny to access this best resource.

5. Is it enough to use the RD Sharma boot to score well in the Determinants chapter?

The RD Sharma Class 12 Chapter 5 Exercise 5.3 is the best solutions guide that provides a deeper understanding of the concept of the determinant. Hence it is enough to help you achieve better scores in the public exam.

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