If `A =a_(1) hat"i"+ b_(1)hat"j"and B=a_(2)hat"i"+b_(2)hat"j"` the condition that they are perpendicula to each other is

Options

A. `(a_(1) )/(b_(1))=-(b_(2))/(a_(2))`
B. `a_(1)b_(1)= a_(2) b_(2)`
C. `(a_(1) )/(b_(1))=-(b_(1))/(b_(2))`
D. None of these

Answer

A

Explanation

(a) For vector to be perpendicular ,dot product should be zero .
`therefore(a_(1)hatj+b,hatj).(a_(2)hati+b_(2)hatj)=0`
or`(a_(1))/(b_(1))=-(b_(2))/(a_(2))`