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?
Which of the following is true?

A

AC=2AB

B

AC=-3AB

C

AC=3AB

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`AB=OB-OA=3a-b-2c`
`AC=OC-OA=9a-3b-6c=3AB`
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)|18 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? B divided AC in ratio

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 three points veca-2vecb+3vecc, 2veca+3vecb-4vecc and -7vecb+10vecc are collinear.

For non-zero vectors veca, vecb and vecc , |(veca xx vecb) .vecc| = |veca||vecb||vecc| holds if and only if

Show that the four points A,B,C,D with position vectors veca,vecb,vecc,vecd respectively, such that 3veca-2vecb+5vecc-6vecd=vec0 , are collinear. Also find the position vector of the point of intersection of the lines Ac and BD.

For any three vectors veca,vecb,vecc show that veca-vecb,vecb-vecc,vecc-veca are coplanar.

prove that : [veca+vecb,vecb+vecc,vecc+veca]=2[veca,vecb,vecc]

Show that points with position vectors 2veca-2vecb+3vecc,-2veca+3vecb-vecc and 6veca-7vecb+7vecc are collinear. It is given that vectors veca,vecb and vecc and non-coplanar.

The non-zero vectors veca,vecb and vecc are related by veca=8vecb and vecc=-7vecb . Then the angle between veca and vecc is :