Determine whether the given vectors are orthogonal, parallel or neither.
<-5,3,7> and <6,-1,2>
<4,6> and <-3,2>
-i + 2j + 5k and 3i + 4j - k
2i + 6j - 4k and -3i -9j +6k
Find a unit vector that is orthogonal to both i+j and i+k.
If a = <3,0,-1>, find a vector b such that comp_a b = 2 (component of b in the a direction is 2).
This solution shows how to check four different pairs of vectors to see if they are orthogonal, parallel, or neither. It also shows how to construct a unit vector orthogonal to two other vectors, and how to construct a vector with a given component in a given direction.