# Homework Help: Vectors Multiplication

1. Oct 23, 2011

### Physics697

Actually I have two questions

1. The problem statement, all variables and given/known data

Vectors A and B are shown on the figure below. Which one of the
following statements is correct?
a) A . B = 0 and A × B ≠ 0
b) A . B ≠ 0 and A × B = 0
c) A . B ≠ 0 and A × B ≠ 0
d) A . B = 0 and A × B = 0
Picture: http://i.imgur.com/X0GB9.png

2. Relevant equations

A.B = AxBx + AyBy

3. The attempt at a solution

Obviously, the answer is zero. but the problem is the difference between A . B and A x B. I have long thought that those two are the same, but this question confused me.
I tried google for a bit and found out that [ dot product (u . v) gives a scalar ] and [ cross product (u x v) gives a pseudovector ]. It's my first time hearing about a pseudovector =_=

My second question is also about Vectors Multiplication

1. The problem statement, all variables and given/known data

A and B are the two vectors shown in the figure. Vector A is along the positive x
axis and has a magnitude of 5 cm, and the vector B is in the x-y plane at an angle 30º
with the positive x axis and has a magnitude of 4 cm. A × B =

a) 20 cm2 in the +x direction b) 10 cm2 in the +y direction
c) 10 cm2 in the +z direction d) 20 cm2 in the -y direction

2. Relevant equations

A.B = AxBx + AyBy

3. The attempt at a solution

When I tried to solve it I got C= 17.5 + 0, so the answer might be a.

This cm^2 and the +z confused me, so I just wanted to confirm.

2. Oct 23, 2011

### 256bits

Here is a re-fresher on dot and cross product.
http://ltcconline.net/greenl/courses/107/vectors/dotcros.htm

For 2 vectors A and B orthoganol ( at right angles) then the dot product A . B = 0, (ie there is no component of A is the same direction as B ( or visa-versa ) sometimes called the projection of A on B.

But, the other part of the answer is A x B = 0 or A x B ≠ 0.

What is your relevant equation for A x B??

Well, you are multiplying a value in A with dimensions cm by one in B of dimension cm, so that would be cm^2.

Axis x and y make a plane,
Add another axis called z and you can work with volumes.
The axis can also be labelled by the unit vectors i,j,k, which you might not have seen yet.

3. Oct 24, 2011