Vectors v and w are sides of an equilateral triangle whose sides have length 1. compute v·w

Solution:

It is given that

Length of v and w = 1

We know that

An equilateral triangle has all three sides of equal lengths and angles which is 60^°.

Φ = 60^°

The equation for the angle between vectors using the dot product of vectors is

(v . w) = |v| |w| cos Φ

The magnitude of the vectors is the length of the vectors given = 1 each.

Substituting the values

(v . w) = cos 60^° × 1 × 1

(v. w) = 1/2

Therefore, v.w is 1/2.

Vectors v and w are sides of an equilateral triangle whose sides have length 1. compute v·w

Summary:

If the vectors v and w are sides of an equilateral triangle whose sides have length 1, then v.w is 1/2.