How Do Dot Product and Cross Product Differ in Vector Multiplication?

[Physics697]

Actually I have two questions

Homework Statement

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

Homework Equations

A.B = AxBx + AyBy

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

Homework Statement

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

Homework Equations

A.B = AxBx + AyBy

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.

 

[256bits]

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

Obviously, the answer is zero.

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??

This cm^2 and the +z confused

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.

 

[Physics697]

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.

Thank you for you reply,
Yeah, I understood the first one thanks to the website you posted.

first question answer: a) A . B = 0 and A × B ≠ 0
and the answer for the second one is ' C= 17.5 + 0 '

Thanks (*