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

A

Explanation

Here A+B=18
Also `A^(2)+B^(2)+2ABcostheta=(12)^(2)=144`
Also `(Bsintheta)/(A+Bcostheta)=tan90^@=oo`
or `A+Bcostheta=0` and `Bcostheta=-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.