Question

What is the formula to find the cosine of the angle between two vectors?

A) dot(V1, V2) / (|V1| * |V2|)
B) |V1| * |V2| / dot(V1, V2)
C) cross(V1, V2) / (|V1| * |V2|)
D) sin(angle) * |V1 - V2|

Answer 1

The formula to find the cosine of the angle between two vectors is: dot(V1, V2) / (|V1| * |V2|).

Step-by-step explanation:

The formula to find the cosine of the angle between two vectors is:

A) dot(V1, V2) / (|V1| * |V2|)

The dot product of two vectors is obtained by multiplying their magnitudes and the cosine of the angle between them. Dividing the dot product by the product of the magnitudes of the vectors gives us the cosine of the angle.

Example:

If we have vectors V1 = [2, 3, 4] and V2 = [-1, 5, 2], the dot product of V1 and V2 is (2 * -1) + (3 * 5) + (4 * 2) = -2 + 15 + 8 = 21. The magnitudes of V1 and V2 are sqrt(2^2 + 3^2 + 4^2) = sqrt(29) and sqrt((-1)^2 + 5^2 + 2^2) = sqrt(30), respectively. Therefore, the cosine of the angle between V1 and V2 is 21 / (sqrt(29) * sqrt(30)).