Finding a unit vector orthogonal to

[tnutty]

Homework Statement

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

I know I can solve this using the cross product of the two. But This chapter is about
dot product and not cross product.

I am not sure how I could go about solving this problem using the properties of a dot product.

This is just a review, in test I would use the cross product.

 

[tnutty]

Thinking about this, I think I could use this formula :

A*B = |A||B| cos(theta);

=

B / |B| = |A|cos(theta) / A

Where A is the displacement vector from the given vector, and theta should be 90 deg.

Thus I would find a unit vector, B, perpendicular to the displacement vector of the
given vectors, which is parallel to Each of the 2 given vector.

Is this assumption correct?