problem with vectors

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February 10th 2009, 01:17 PM
sillyme

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)|
February 10th 2009, 01:50 PM
Plato

Quote:

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 $u\times v$ ?
Or is it a dot product: $u \cdot v$ ?
I suspect it is a dot product.
February 10th 2009, 02:12 PM
sillyme

Quote:

Originally Posted by Plato

Is that a cross product $u\times v$ ?
Or is it a dot product: $u \cdot v$ ?
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)

$p = |(a+b)\times (a-b)|$
February 10th 2009, 02:26 PM
o_O
Some useful properties:
- $(u + v) \times w = (u \times w) + (v \times w)$
- $w \times (u + v) = (w \times u) + (w \times v)$
- $u \times v = -(v \times u)$
- $|u \times v | = |u||v|\sin \theta$
So:

But since they're orthogonal ....
February 10th 2009, 02:37 PM
sillyme

Thank you o_O.
February 11th 2009, 06:56 AM
HallsofIvy

A very simple way to do this is to set up a coordinate system so the $\vec{a}= 3\vec{i}$ and $\vec{b}= 4\vec{j}$ .
Then $\vec{a}+ \vec{b}= 3\vec{i}+ 4\vec{j}$ , $\vec{a}- \vec{b}= 3\vec{i}- 4\vec{j}$ , $3\vec{a}- \vec{b}= 9\vec{i}- 4\vec{j}$ , and $\vec{a}- 2\vec{b}= 3\vec{i}-8\vec{j}$ .