Vector HW

1. Consider a set of vectors:

A = 2i - 4j + 12k

B = 6i + 2j - 8k

Find the following:

A + B
B - A
the magnitude of each vector
the angle between the vectors

2. We didn't get into cross products seriously. Here's the brief definition: the cross product of 2 vectors is a third vector (perpendicular to the plane of the original 2 vectors; described by the right hand rule). The vector has magnitude given by:

A X B = A B sin(phi)

When you take the cross product of 2 vectors, you foil them (as we did for the dot product). However, doing the cross product of unit vectors (i, j, k) is trickier to determine. There is a simple way to remember this, but it's hard to describe in print - I'll show you Wednesday. Until then, here's the general answers:

i x j = k
j x k = i
k x i = j
i x k = -j
k x j = -i
j x i = -k

With this in mind, take the cross product of the two vectors above - the answer will be a vector (with i, j, and k components).

3. For fun:

If you understand the right hand rule, try these:

UP X WEST

BACKWARDS X DOWN

4. As always, be caught up on reading, etc.