Find the dot product of vectors cd if | c | = 3, | b | = 2, and the angle between the vectors is 135 °

1. Definition of the dot product of vectors:

The scalar product of two vectors a and b will be a scalar value equal to the product of the moduli of these vectors multiplied by the cosine of the angle between them (cos c):

a * b = | a | * | b | * cos c

2. Substitute into the formula the values from the condition: c * d = | c | * | d | * cos 135 ° c * d = 3 * 2 * cos 135 ° c * d = 3 * 2 * (- 2 ^ (1/2) / 2) c * d = – 3 * 2 ^ (1/2) or approx * d = – 4.24 Answer: c * d = – 3 * 2 ^ (1/2) ~ – 4.24