Question

Find the vector `vecb`, orthogonal to `veca=6hati+4hatj`?

Answer 1

`vecb=-4/sqrt13hati+6/sqrt13hatj` or `vecb=4/sqrt13hati-6/sqrt13hatj`

Explanation:

Let `vecb=xhati+yhatj` and as `veca=6hati+4hatj`

Then `veca*vecb=6x+4y`, but as `veca` and `vecb` are orthogonal their dot product should be `0` i.e. `6x+4y=0` or `6x=-4y` or `x=-2/3y` i.e.`vecb=-2/3yhati+yhatj` and hence `|b|=sqrt((4y^2)/9+y^2)=sqrt((13y^2)/9)`

As `|b|=2`, `(13y^2)/9=4`

or `y=+-6/sqrt13` and `x=∓4/sqrt13`

Hence `vecb=-4/sqrt13hati+6/sqrt13hatj` or `vecb=4/sqrt13hati-6/sqrt13hatj`