Checking and Constructing Orthogonal or Parallel Vectors

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).

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Solution Summary

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.