Vectors and the Geometry of Space

Question

You are looking down at a map. A vector u with |u| = 10 points north and a vector v with |v| = 6 points northeast. The crossproduct u×v points:

The magnitude |u×v| =

Answer 1

for finding The magnitude |u×v| we will use |u×v| = |u| |v| sin ∅

∅ will be 45º in this situation because the northeast is in the middle of the north and east.

|u×v| = 10*6 sin 45º

= 60 sin45º

= 60*0.707

= 42.42

Answer 2

|| u × v || = || u|| ||v|| sin θ

The only piece left for you is to determine the angle θ