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Math Help - Vectors, dot product and cross product. URGENT please Help

  1. #1
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    Vectors, dot product and cross product. URGENT please Help

    1) Vector v has magnitude 10 units, positive, and equal x and y components, and a z component of 4. Determine V.

    2) vector u is give as u= (1, -2, 1)
    a) determine 3 different non-collinear vectors perpindicular to u.
    b) show that the 3 vectors in part a are coplanar

    3) prove that (a-b)x(a+b) = 2(axb)

    4) Find total work done by 15 N force, F, in the direction of the vector, (1,2,2) when it moves a particle from O(0,0,0) to P(1, -3, 4) and then from P to Q(7,2,5). The distance is measure in metres.
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi
    Quote Originally Posted by xkissesx View Post
    1) Vector v has magnitude 10 units, positive, and equal x and y components, and a z component of 4. Determine V.
    V=\begin{pmatrix}x\\y\\z\end{pmatrix}

    We know that x=y and z=4 hence V=\begin{pmatrix}x\\x\\4\end{pmatrix}. Then, \|V\|=10 gives an equation that can be solved for x... and knowing x, you can determine V.

    2) vector u is give as u= (1, -2, 1)
    a) determine 3 different non-collinear vectors perpindicular to u.
    For any two vectors a and b, a\times b\perp a. (and a\times b\perp b)
    b) show that the 3 vectors in part a are coplanar
    How can one define a plane with a dot and a vector ?
    3) prove that (a-b)x(a+b) = 2(axb)
    Cross product distributes over addition : u\times(v+w)=u\times v+u\times w
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