Calculus

Dot Product

1. Compute the dot product ~a ·~b if ~a = 6̂i− 10ĵ + 10k̂ and ~b = −7̂i− 4ĵ − 3k̂.

2. Find < 0, 3, 7 > · < 2,−3, 7 >.

3. If ~v · ~w = 2, ||~v|| = 5, and ||~w|| = 9, what is the value of 3~v · (2~v − 3~w)?

4. Given the points A = (10, 5), B = (5, 7), and C = (1, 9). Use dot product to find the

cosine of the angle between ~AB and ~BC.

5. Use dot product to show that the angle between < a,b,c > and < −a,−b,−c > (opposite facing vectors) is π.

6. Find the values of x such that the vectors < 3, 2,x > and < 2x, 4,x > are orthogonal.