00:01
Hi there, we have two pairs of vectors here and we are to evaluate the given cross products.
00:07
For part a, vector a is going to the right at six units and vector b is four units.
00:16
Angle between them is 45.
00:18
So let's call the angle between the two vectors as angle phi.
00:22
Angle phi here is 45.
00:24
So cross product, we get first the magnitude of the cross product of a with b, and that's just given by the magnitude of a times the magnitude of b times the sign of the angle between them.
00:40
So we have everything we need.
00:42
It's just six times four times the sign of angle 45.
00:49
So the magnitude here in two significant figures is 17.
00:55
For the direction we will use the right hand rule so for the right hand rule let me show the three dimensional axis here oops let's write it properly so our two vectors here are on the xy plane let's use the horizontal as our x axis vertical as the y and the third axis that cuts through the xy plane is the z -axis.
01:30
So let's sketch tail -to -tail the two vectors.
01:33
We have a going to the right and then b in the second quadrant here in the x -y plane.
01:42
So for the right -hand rule, we will curl our right hand into the direction of the first vector, going to direction of the second vector.
01:52
So that would mean if you curl your right fingers from a to b, the rotation, the curling of your four fingers will be counterclockwise, and your thumb will be pointing in this direction along the positive z axis.
02:11
So the curved direction of the curling of the four fingers in the right hand is the direction of rotation from a to b.
02:20
And then your thumb points the direction of the cross product...