Home
Class 12
MATHS
Three points A,B, and C have position ve...

Three points A,B, and C have position vectors `-2veca+3vecb+5vecc, veca+2vecb+3vecc` and `7veca-vecc` with reference to an origin O. Answer the following questions?
B divided AC in ratio

A

`2:1`

B

`2:3`

C

`2:-3`

D

`1:2`

Text Solution

Verified by Experts

The correct Answer is:
D
`because 2OA-3OB=OC=0`

`implies OB=(2OA+OC)/(3)`
`implies B` Divides AC in 1:2.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|1 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|7 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|3 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|19 Videos

Similar Questions

Explore conceptually related problems

Three points A,B, and C have position vectors -2veca+3vecb+5vecc, veca+2vecb+3vecc and 7veca-vecc with reference to an origin O. Answer the following questions? Which of the following is true?

Three points A,B, and C have position vectors -2veca+3vecb+5vecc, veca+2vecb+3vecc and 7veca-vecc with reference to an origin O. Answer the following questions? Which of the following is true?

A, B, C and D have position vectors veca, vecb, vecc and vecd , repectively, such that veca-vecb = 2(vecd-vecc) . Then

Show that the points veca+2vecb+3c-2veca+3vecb+5vecc and 7veca-vecc are colinear.

Prove th the following sets of three points are collinear: -2veca+3vecb+5vecc, veca+2vecb+3vecc, 6veca-vecc

Show that the three points whose position vectors are veca-2vecb+3vecc, 2veca+3vecb-4vecc, -7vecb+10vecc are collinear

For any three vectors veca, vecb, vecc the value of [(veca-vecb, vecb-vecc, vecc-veca)] , is

For any three vectors veca, vecb, vecc the value of [(veca+vecb,vecb+vecc,vecc+veca)] is

for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) = 2 veca.vecb xx vecc .

Consider three vectors veca, vecb and vecc . Vectors veca and vecb are unit vectors having an angle theta between them For vector veca, |veca|^2=veca.veca If veca_|_vecb and veca_|_vecc then veca||vecbxxvecc If veca||vecb, then veca=tvecb Now answer the following question: If vecc is a unit vector and equal to the sum of veca and vecb the magnitude of difference between veca and vecb is (A) 1 (B) sqrt(2) (C) sqrt(3) (D) 1/sqrt(2)