Finding dot product, cross, and angle between 2 vectors

[PAstudent]

Homework Statement

[/B]
Vector A lies in the yz plane 63.0 degrees from the +y axis, has a positive z component, and has a magnitude 3.20 units. Vector B lies in the xz 48.0 degrees from the +x axis, has positive z component, and has magnitude 1.40 units.

a) find A dot B
b) find A x B
c) the angle between A and B

Homework Equations

dot product and cross product [/B]

The Attempt at a Solution

What I am trying is to put them in unit vector notation like:
A= axi+ayj so A= [3.20cos(63.0)]i+[3.20sin(63.0)] and then the same for vector B

Then once I have those components I could easily do dot and cross product. My question is what does that "has a positive z component " have to do with anything? And is my setup correct?[/B]

 

[SteamKing]

Homework Statement

[/B]
Vector A lies in the yz plane 63.0 degrees from the +y axis, has a positive z component, and has a magnitude 3.20 units. Vector B lies in the xz 48.0 degrees from the +x axis, has positive z component, and has magnitude 1.40 units.

a) find A dot B
b) find A x B
c) the angle between A and B

Homework Equations

dot product and cross product [/B]

The Attempt at a Solution

What I am trying is to put them in unit vector notation like:
A= axi+ayj so A= [3.20cos(63.0)]i+[3.20sin(63.0)] and then the same for vector B

Then once I have those components I could easily do dot and cross product. My question is what does that "has a positive z component " have to do with anything? And is my setup correct?[/B]

For example, vector B could make an angle of 48° above or below the +x-axis. The "positive z-component" tells you which side of the +x-axis to draw this vector.

I find in these cases making a simple sketch usually clarifies things a bit.

 

[PAstudent]

So would there be a z hat in the calculations of the dot and cross or does it just tell you the location of the vector? Because I am still trying to figure out how to find the i and j to be able to find the products

 

[SteamKing]

So would there be a z hat in the calculations of the dot and cross or does it just tell you the location of the vector? Because I am still trying to figure out how to find the i and j to be able to find the products

It seems you have three-dimensional vectors here, but I haven't sketched them out or anything. You'll have to work thru the verbal descriptions, and make some sketches as I suggested.