Question

You are looking down at a map. A vector u with |u| = 6 points north and a vector v with |v| = 5 points northeast. The crossproduct u×v points:
(A) south
(B) northwest
(C) up
(D) down
(E) The magnitude |u×v| =

Answer 1

Answer: Hi!

First, UxV = sin(a)*IUI*IVI

where a is the angle between U and V, in this case 45°.

First, the cross product of UxV points:

Here you can use the right hand method,

Put your hand flat, so the point of your fingers point in the same direction that the first vector, in this case U, so your fingers will point to the north.

Now roll your fingers in the direction of the second vector, so here you will roll your fingers in the northeast direction. Now you will see that your thumb is pointing down, so the cross product of UxV points down.

And the magnitude is 6*5*sin(45) = 21.213