# Thread: Dot product and Angle

1. ## Dot product and Angle

This is a question from calculus 3 class.

"Find the dot product of the vectors and the cosine of the angle between them."

u = i - 3j + 7k
v = 8i - 2j - 2k

Okay, I get what to do, and I get answers but apparently they're wrong according to the back of the book. What am I doing wrong?

My work:
u dot v = (1*8) + (-3*-2) + (7*-2) = 28 = dot product

||u|| = sqrt(1^2 + (-3)^2 + 7^2) = sqrt(59)
||v|| = sqrt(8^2 + (-2)^2 + (-2)^2) = 6*sqrt(2)

(28) / ( sqrt(59) * (6*sqrt(2)) ) = .429601
cos^-1 (.429601) = 1.12675 radians = angle

Edit: The book says the dot product is 0 and the angle is also 0.

2. (1*8) + (-3*-2) + (7*-2) = 8 + 6 - 14 = 0.

If the book says that the angle is also 0, they're wrong. But if, as I suspect, they mean that the cosine of the angle is zero, they'd be correct.

3. Ahh I see.. I added 14 for some reason.. even though I went through this 3 times already. :| I think I got the angle working too now.

Thanks!

4. No problem. Have a good one!