Multi-Variable Calculus: Cross Product Expressions

  1. Dembadon

    Dembadon 666
    Gold Member

    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|
  2. jcsd
  3. Dick

    Dick 25,913
    Science Advisor
    Homework Helper

    Check 3. What's the length of |u|v?
  4. Dembadon

    Dembadon 666
    Gold Member

    [STRIKE]If |u| = k, where k is some constant, then the length of |u|v would be kv1 + kv2.[/STRIKE]


    I think I see my mistake. It should be [tex]\frac{\vec{u}}{|\vec{u}|}\vec{v}[/tex].
    Last edited: Sep 8, 2011
  5. wukunlin

    wukunlin 386
    Gold Member

    you might want to check again
  6. Dembadon

    Dembadon 666
    Gold Member

    [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].
  7. lanedance

    lanedance 3,307
    Homework Helper

    looks good
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