Home
Class 12
MATHS
If a,b and c are three non-zero vectors ...

If a,b and c are three non-zero vectors such that no two of these are collinear. If the vector a+2b is collinear with c and b+3c is collinear with a(`lamda` being some non-zero scalar), then a+2b+6c is equal to

A

0

B

`lamdab`

C

`lamdac`

D

`lamda a`

Text Solution

Verified by Experts

The correct Answer is:
A
As `a+2b` and c are collinear a+2b=`lamdac` . . (i)
Again, b+3c is collinear with a. ltbr. `therefore b+3c=mua` . . . (ii)
Now, `a+2b+6c=(a+2b)+6c=lamdac+6c`
`=(lamda+6)c` . . (iii)
Also, `a+2b+6c=a+2(b+3c)=a+2mua`
`=(2mu+1)a` . . . (iv)
From eqs. (iii) and (iv), we get
`(lamda+6)c=(2mu+1)a`
but a and c are non-zero non-collinear vectors,
`thereforelamda+6=0=2mu+1`
Hence, `a+2b+6c=0`.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 2|17 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

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

Similar Questions

Explore conceptually related problems

Let veca,vecb, and vecc be three non zero vector such that no two of these are collinear. If the vector veca+2vecb is collinear with vecc and vecb+3vecc is colinear with veca (lamda being some non zero scalar) then veca\+2vecb+6vecc equals (A) lamdaveca (B) lamdavecb (C) lamdavecc (D) 0

If bara,barb and barc be there non-zero vectors, no two of which are collinear. If the vectors bara+2barb is collinear with barc and barb+3barc is collinear with a, then ( lambda being some non-zero scalar) bara+2barb+6barc is equal to

Let a,b and c be three non-zero vectors which are pairwise non-collinear. If a+3b is collinear with c and b+2c is collinear with a, then a+3b+6c is

Let vec a,vec b and vec c be three non-zero vectors, no two of which are collinear.If the vector 3vec a+7vec b is collinear with vec c and 3vec b+2vec c is collinear with bar(a), then 9vec a+21vec b+14vec c is equal to.

Let bar(a),bar(b) and bar(c) be three non-zero vectors,no two of which are collinear.If the vectors bar(a)+2bar(b) is collinear with bar(c) and bar(b)+3bar(c) is collinear with bar(a), then bar(a)+2bar(b)+6bar(c) is equal to