Question

Find the dot product of two vectors if their lengths are 4 and 1/2 and the angle between them is π/4.

Answer 1

The dot product is a technique that solves the resultant vector through the use of matrices. Since we have no coordinates, we can't use matrices. However, we can still solve the resultant vector (red line) through cosine law. The solution is as follows:

R² = 4² + (1/2)² - 2(4)(1/2)(cos π/4)
R = √13.42
R = 3.66

The resultant vector has a magnitude of 3.66.