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

`lamda a`

B

`lamdab`

C

`lamda c`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
D
If a+2b is collinear with c, then a+2b=tc . . . (i)
also, b+3c is collinear with a, then
`b+3c=lamda a`
`implies b=lamda a-3c` . . (ii)
from eqs. (i) and (ii), we get
`a+2(lamda a-3c)=tc`
`implies (a-6c)=tc-2lamda a`
on comparing the coefficient of a and c, we get
`1=-2lamda implies lamda=-(1)/(3)`
and `-6=t implies t=-6`.
From eq. (i) we get,
`a+2b=-6c` ,brgt `implies a+2b+6c=0`
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Subjective Type Questions)|8 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

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

Similar Questions

Explore conceptually related problems

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, vec c be three non-zero vectors such that any two of them are non-collinear. If vec a+2 vec b is collinear with vec ca n d vec b+3 vec c is collinear with vec a then prove that vec a+2 vec b+6 vec c= vec0

veca,vecb and vecc are three non-zero vectors, no two of which are collinear and the vectors veca+vecb is collinear with vecc , vecb+vecc is collinear with veca , then veca+vecb+vecc=

If vec a , vec b, vec c are three non- null vectors such that any two of them are non-collinear. If vec a+ vec b is collinear with vec ca n d vec b+ vec c is collinear with vec a , then find vec a+ vec b+ vecc

If veca, vecb and vecc are three non-zero vectors, no two of which are collinear, veca +2 vecb is collinear with vecc and vecb + 3 vecc is collinear with veca , then find the value of |veca + 2vecb + 6vecc| .

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

If a, b and c are any three non-zero vectors, then the component of atimes(btimesc) perpendicular to b is

If vec a ,\ vec b ,\ vec c are three non-zero vectors, no two of which are collinear and the vector vec a+ vec b is collinear with vec c ,\ vec b+ vec c is collinear with vec a ,\ t h e n\ vec a+ vec b+ vec c= vec a b. vec b c. vec c d. none of these

Let veca,vecb,vecc be three non zero vectors which are pairwise non colinear. If a + 3b is collinear with c and b+2c is collinear with a, then a + 3b + 6c is equal to (A) a+c (B) a (C) c (D) 0

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.