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Multi-Variable Calculus: Cross Product Expressions

by Dembadon
Tags: calculus 3, cross product, vectors
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Dembadon
#1
Sep7-11, 10:26 PM
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I would like to check my answers...

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

Given nonzero vectors u, v, and w, use dot product and cross product notation to describe the following.
  1. A vector orthogonal to u X v and u X w
  2. A vector orthogonal to u + v and u - v
  3. A vector of length |u| in the direction of v
  4. The area of the parallelogram determined by u and w

2. Relevant equations



3. The attempt at a solution
  1. (u X v) X (u X w)
  2. (u + v) X (u - v)
  3. |u|v
  4. |u X w|
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Dick
#2
Sep7-11, 10:47 PM
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Check 3. What's the length of |u|v?
Dembadon
#3
Sep7-11, 11:19 PM
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Quote Quote by Dick View Post
Check 3. What's the length of |u|v?
If |u| = k, where k is some constant, then the length of |u|v would be kv1 + kv2.

Hmm..

I think I see my mistake. It should be [tex]\frac{\vec{u}}{|\vec{u}|}\vec{v}[/tex].

wukunlin
#4
Sep7-11, 11:27 PM
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Multi-Variable Calculus: Cross Product Expressions

Quote Quote by Dembadon View Post
If |u| = k, where k is some constant, then the length of |u|v would be kv1 + kv2.

Hmm..

I think I see my mistake. It should be [tex]\frac{\vec{u}}{|\vec{u}|}\vec{v}[/tex].
you might want to check again
Dembadon
#5
Sep7-11, 11:51 PM
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[itex]\frac{\vec{v}}{|\vec{v}|}[/itex] is a unit vector in the direction of [itex]\vec{v}[/itex]. I need to multiply the unit vector by [itex]|\vec{u}|[/itex].

So, [itex]|\vec{u}|\frac{\vec{v}}{|\vec{v}|}[/itex].
lanedance
#6
Sep8-11, 12:52 AM
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looks good


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