Question

Find a · b. |a| = 60, |b| = 30, the angle between a and b is 3π/4.

Answer 1

The dot product is used to determine the magnitude of the resultant vector of two component vectors. It is expressed as a·b. It does not literally mean that you multiply their values. Instead, you multiply their matrices. However, since we cannot find matrices, let's just find the resultant vector through theorems involving triangles. By cosine law:

R = √[a² + b² - 2abcos(3π/4)]
R = √[60² + 30² - 2*60*30*cos(3π/4)]
R = 83.94

Thus, a·b = 83.94