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Answer:

Yes, unless the two vectors are parallel.

Two Vectors Define a Plane

You may recall from high school geometry that two lines (not colinear) define a plane. This is the same thing. Most of the examples in this chapter start with two 2D vectors. However, the results are valid for two 3D vectors because you can find a plane that contains them both.

The figure shows a vector w and an arbitrary vector v. For convenience in visualization, their tails start from the same point (but, of course, vectors have no position).

Also for convenience, the vector v is horizontal; but it could be at any orientation.

QUESTION 3:

Does the scaled vector kv (where k is a scalar) have the same orientation as v?