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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).


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.