RD Sharma Solutions Class 12 Algebra of Vectors Exercise 23.4

RD Sharma Solutions for Class 12 Maths Chapter 23 Algebra of Vectors Exercise 23.4 are given here to help students prepare for their exams at ease. Practising the textbook problems will primarily benefit the students to analyse their level of preparation and also assess their conceptual knowledge. Students can now easily download the RD Sharma Class 12 Solutions PDF of this exercise for free, from the link given below.

RD Sharma Solution for Class 12 Maths Chapter 23 Exercise 4

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Access Answers for RD Sharma Solution Class 12 Maths Chapter 23 Exercise 4

Exercise 23.4

1. Solution:

Given,

In ∆ABC, D, E and F are the mid-points of the sides of BC, CA and AB, respectively. And O is any point in space.

Let
be the position vectors of points A, B, C, D, E and F with respect to O.

So,

2. Solution:

Required to prove: The sum of the three vectors determined by the medians of a triangle directed from the vertices is zero.

Let ABC be a triangle such the position vector of A, B, and C are
respectively.

As AD, BE, and CF are medians

Then, D, E and F are mid-points

So, we have

3. Solution:

Given, ABCD is a parallelogram and P is the point of intersection of diagonals, and O is the point of reference.

4. Solution:

Let’s consider ABCD to be a quadrilateral and P, Q, R and S to be the mid-points of sides

Let ABCD be a quadrilateral and P, Q, R and S be the midpoints of sides AB, BC, CD and DA, respectively.

Let the position vector of A, B, C and D be

So, these are the position vector of P, Q, R and S, respectively.

Now,

Thus, PQRS is a parallelogram, and hence, PR bisects QS.

Therefore, the line segment joining the midpoint of opposite sides of a quadrilateral bisect each other.

5. Solution:

Let
be the position vectors of the points A, B, C and D, respectively.

Then position vector of

Q is the midpoint of the line joining the midpoints of AB and CD.

Hence,