Thread: problem with vectors

I need some help with the the following problem:

If vectors a and b are orthogonal, |a|=3, |b|=4.
Calculate:
a) p=|(a+b)x(a-b)|
b) q=|(3a-b)x(a-2b)|

Originally Posted by sillyme

I need some help with the the following problem:
If vectors a and b are orthogonal, |a|=3, |b|=4.
Calculate:
a) p=|(a+b)x(a-b)|
b) q=|(3a-b)x(a-2b)|

Is that a cross product ?
Or is it a dot product: ?
I suspect it is a dot product.

Originally Posted by Plato

Is that a cross product ?
Or is it a dot product: ?
I suspect it is a dot product.

It is a cross product.
p is the norm of the cross product between the vector sum (a+b) and the vector difference (a-b)

Some useful properties:

• 
• 
• 
• 

So:

But since they're orthogonal ....

Thank you o_O.

A very simple way to do this is to set up a coordinate system so the and .
Then , , , and .