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Equilateral Triangle: Vectors

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See the attachment for a diagram of an equilateral triangle with sides u, v and w. U is a unit vector. Find u dot v and u dot w (u.v and u.w).

The answers are: u.v = 1/2, and u.w = -1/2.

Why is u.w a minus 1/2?

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Solution Summary

The solution finds u dot v and u dot w (u.v and u.w) from the diagram provided.

Solution Preview

From the diagram we see that:

u + w = v


w = v - u


u.w = u.(v-u)

Because the dot product is distributive:

u.w = u . (v-u) = u.v - u.u

We know ...

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