R D Sharma Solutions for Chapter: Algebra of Vectors, Exercise 3: EXERCISE

Author:R D Sharma

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: Algebra of Vectors, Exercise 3: EXERCISE

Attempt the free practice questions on Chapter 4: Algebra of Vectors, Exercise 3: EXERCISE with hints and solutions to strengthen your understanding. MATHEMATICS CLASS XII VOLUME-2 solutions are prepared by Experienced Embibe Experts.

Questions from R D Sharma Solutions for Chapter: Algebra of Vectors, Exercise 3: EXERCISE with Hints & Solutions

MEDIUM
12th CBSE
IMPORTANT

Find the position vector of a point R which divides the line joining the two points P and Q with position vectors OP=2a+b and OQ=a-2b respectively in the ratio 1 : 2 internally and externally.

HARD
12th CBSE
IMPORTANT

Let a, b, c, d be the position vectors of the four distinct points A, B, C, D. If b-a=c-d then show that ABCD is a parallelogram.

HARD
12th CBSE
IMPORTANT

If a, b are the position vectors of A, B respectively, find the position vector of a point C in AB produced such that AC=3 AB and that a point D in BA produced such that BD=2 BA.

HARD
12th CBSE
IMPORTANT

Show that the four points A,B,C,D with position vectors a,b,c,d respectively such that 3a-2b+5c-6d=0, are coplanar. Also, find the position vector of the point of intersection of the line segments AC and BD.

HARD
12th CBSE
IMPORTANT

Show that the four points P,Q,R,S with position vectors p,q,r,s respectively such that 5p-2q+6r-9s=0,are coplanar. Also, find the position vector of the point of intersection of the line segments PR and QS.

HARD
12th CBSE
IMPORTANT

The vertices A,B,C of triangle ABC have respectively position vectors a,b,cwith respect to a given origin O. Show that the point D where the bisector of A meets BC has position vector d=βb+γcβ+γ, where β=c-a and, γ=a-b.Hence, deduce that the incentre I has position vector αa+βb+γcα+β+γ, where α=b-c.