Question

Find a unit vector that is orthogonal to both i+j and i+k

Answer 1

Finding the orthogonal vector is simple: just use the cross-product, (i+j) x (i+k).

Once you calculate that, just take its length and divide by that, and you'll naturally have a unit vector.

Answer 2

what if i have to find it using only the dot product or the propeties of vectors