Guest

a,b,c are three non zero vectors no two of which are collinear If the collinear .If the vectors a+2b is the collinear with c and b+3c is collinear with a,a+2b+6c is equal to

a,b,c are three non zero vectors no two of which are collinear If the collinear .If the vectors a+2b is the collinear with c and b+3c is collinear with a,a+2b+6c is equal to

Grade:12

3 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear pallavi

let a+2 b = u c  ............1

and   b+3c =va ............2

put replace vctor a from 1 and b

 b+3c =v(uc-2b)

or  (1+2v)b=(uv-3)c

since b and c are not colinier so

 1+2v =0   or v=-1/2

and uv-3=0   or u=-6

put value of u in equation 1

a+2b=-6c

a+2b+6c=0

Please feel free to post as many doubts on our discussion forum as you can.
 If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.

 All the best.
 
Regards,
Askiitians Experts
Badiuddin

Viraj Jorapur
16 Points
14 years ago
Let a+2b=kc b+3c=qa From the first equation, we get, b=(kc-a)/2 Substituting in the other equation, we get (k+6)c=(2q+1)a But as these vectors are not collinear, so the L.H.S. and R.H.S. must be equal to zero independently. So we get (k+6)=0 k=-6 So a+2b= -6c a+2b+6c=0
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the attached answer to your question below.
 
let a+2 b = u c  ............1
and   b+3c =va ............2
put replace vector a from 1 and b
b+3c = v(uc-2b)
or  (1+2v)b=(uv-3)c
since b and c are not colinier so
 1+2v =0   or v=-1/2
and uv-3=0   or u=-6
put value of u in equation 1
a+2b=-6c
a+2b+6c=0
 
Hope it helps.
Thanks and regards,
Kushagra

Think You Can Provide A Better Answer ?

ASK QUESTION

Get your questions answered by the expert for free