Home
Class 12
MATHS
Let a,b and c be three non-zero vectors ...

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

A

a+c

B

a

C

`c`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
As, a+3b is collinear with c.
`thereforea+3b=lamdac` . . . (i)
Also, b+2c is collinear with a.
`implies b+2c=mua` . . (ii)
From eq. (ii), we get
`a+3b+6c=(lamda+6)c` . .. (iii)
From eq. (ii), we get
`a+3b+6c=(1+3mu)a` . . (iv)
From eqs. (iii) and (iv), we get
`therefore(lamda+6)c=(1+3mu)a`
Since, a is not collinear with c.
`implies lamda+6=1+3mu=0`
from eq. (iv), we get
`a+3b+6c=0`.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|8 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 a,b,c be three non-zero vectors which are pairwise non-collinear.If a+3b is collinear with cand c and b+2c is collinear with a then a+b+6c is

If bara,barb,barc are three non-zero vectors which are pairwise non-collinear. If bara+3barb is collinear with barc and barb+2barc is collinear with bara , then bara+3barb+6barc is

Let bar(a) , bar(b) , bar(c) be three non- zero vectors which are pair-wise non- collinear.If bar(a)+3bar(b) is collinear with bar(c) and bar(b)+2bar(c) is collinear with bar(a) , then bar(a)+3bar(b)+6bar(c)=...........

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

If vec a,vec b and vec c are three non-zero vectors,no two of which ar collinear,vec a+2vec b is collinear with vec c and vec b+3vec c is collinear with vec a then find the value of |vec a+2vec b+6vec c|