Vector `vec(a)` has components `a_(x)=3, a_(y)=4`. Find the components of a vector `vec(c)` which is perpendicular to `vec(a)` and has a magnitude of `5` units.

Answer

`c_(x)=+- 4, c_(y)=+-3`

Explanation

Let `vec(c)` is `=c_(x)hat(i)+c_(y)hat(j)`
then according to question `=sqrt(c_(x)^(2)+c_(y)^(2))=5`
`rArr c_(x)^(2)+c_(y)^(2)=25` …(i)
and `vec(a), vec(c)=0rArr 3 c_(x)+4 c_(y)=0-` …(ii)
from equation (i) and (ii) `c_(x)=+- 4, c_(y)= +- 3`