Home
Class 12
MATHS
Given three vectors vec a=6 hat i-3 hat...

Given three vectors ` vec a=6 hat i-3 hat j , vec b=2 hat i-6 hat ja n d vec c=-2 hat i+21 hat j` such that ` vecalpha= vec a+ vec b+ vec c ` Then the resolution of the vector ` vecalpha` into components with respect to ` vec a` a n d `vec b` is given by

A

3a-2b

B

3b-2a

C

2a-3b

D

a-2b

Text Solution

Verified by Experts

The correct Answer is:
C
`alpha=a+b+c=6hati+12hatj`
Let `alpha=xa+ybimplies 6x+2y=6`
and `-3x-6y=12`
`therefore x=2,,y=-3`
`therefore alpha=2a-3b`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find vec a +vec b if vec a = hat i - hat j and vec b =2 hat i

let vec a = 2hat i +3hat j and vec b = hat i +4hat j then find projection of vec a on vec b

If the vectors vec a = 2i+3j+6k and vec b are collinear and |vec b| = 21 , then vec b =

if vec a= 2 hat i+ lambda hat j+ hat k and vec b= hat i+ 2 hat j+ 3 hat k are orthogonal then the value of lambda

If veca = 2 hat i + 3 hat j - hat k , vec b = hat i + 2 hat j - 5 hat k, vec c= hat 3i + 5 hatj = hat k , then a vector perpendicular to vec a and in the plane containing vec b and vec c is

Find the angle between the vectors vec(a) = hat(i) + hat(j) + hat(k) and vec(b) = hat(i) - hat(j) + hat(k) .

Let vec a = i-j, vec b = j-k, vec c = k-i . If vec d is a unit vectors such that vec a. vec d = 0 = [vec b vec c vec d] , then vec d =