The sum of the magnitude of two vectors is 18. The magnitude of their resultant is 12. If the resultant is perpendicular to one of the vectors, then the magnitudes of the two vectors are :

Options

A. 5 and 13
B. 6 and 12
C. 7 and 11
D. 8 and 10.

Answer

C

Explanation

HereA + B = 18
Also `A^(2) + B^(2) + 2AB costheta = (12)^(2) = 144`
or A + `B cos theta = 0` and `B cos theta = -A`
Putting above `A^(2) + B^(2)` + 2A (-A) = 144
or `B^(2) -A^(2)= 144`
or (B-A) (B+A)= 144
or 18 (B - A) = 144 or B - A= 8
Now B + A = 18 and B - A = 8.
Solving, we get B = 13 and A= 5.