G Vectors ???? and ???? are sides of an equilateral triangle whose sides have length 4. Compute ????⋅????. (Give your solution as a number to one decimal place.

Question

asked Oct 13, 2022 15.8k views

1 Answer

Rui Marques · Answer 1 · 2022-10-19T20:54:15+0000

Answer:

$v \cdot w = 8.0$

Explanation:

See comment for complete question

Given

|v| = |w| = 4 --- the side lengths

Required

$v \cdot w$

$v \cdot w = |v| \cdot |w| \cdot (cos\theta)$

From the question, we understand that v and w are sides of an equilateral triangle.

This means that:

$\theta = 60^o$ --- angles in an equilateral triangle

So:

$v \cdot w = |v| \cdot |w| \cdot (\cos 60)$

So, we have:

$v \cdot w = 4 * 4 * 0.5$

$v \cdot w = 8.0$