If `vec P = a_(1) hati +a_(2) hatj and vec Q =b_(1) hati+b_(2)hatj` are perpendicular to each other, then

Options

A. `a_(1)b_(1)=a_(2)b_(2)`
B. `(a_(1))/(a_(2))=-(b_(2))/(b_(1))`
C. `a_(1)a_(2)=b_(1)b_(2)`
D. `(a_(1))/(b_(1))=(a_(2))/(b_(2))`

Answer

B

Explanation

If `vec P bot vec Q" then "vec P cdot vec Q=0`
`therefore (a_(1) hati+a_(2)hatj) cdot (b_(1)hati+b_(2)hatj)=0`
`therefore a_(1)b_(1) + a_(2) b_(2) =0" "therefore a_(1)b_(1) =-a_(2)b_(2)`
`therefore (a_(1))/(a_(2)) =-(b_(2))/(b_(1))`