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

Similar Questions

Explore conceptually related problems

Let a,b,c are three vectors of which every pair is non-collinear, if the vectors a+b and b+c are collinear with c annd a respectively, then find a+b+c.

If veca and vecb are two non- zero collinear vectors then …… is correct .

Let a,b and c be three unit vectors such that 3a+4b+5c=0 . Then which of the following statements is true?

If a and b are two non-zero and non-collinear vectors then a+b and a-b are

The number of unit vectors which are collinear with non zero vector bar(a) is ……………

If a,b and c are non-coplanar vectors, prove that 3a-7b-4c, 3a-2b+c and a+b+2c are coplanar.

If a,b and c are non-coplanar vectors and lamda is a real number, then the vectors a+2b+3c,lamdab+muc and (2lamda-1)c are coplanar when

a and b are non-collinear vectors. If c=(x-2) a+b and d=(2x+1)a-b are collinear vectors, then the value of x= . . .

If a,b,c are three non-coplanar vectors, then 3a-7b-4c,3a-2b+c and a+b+lamdac will be coplanar, if lamda is

If a,b and c are non-coplanar vectors, then prove that the four points 2a+3b-c,a-2b+3c,3a+4b-2c and a-6b+6c are coplanar.