• May 14th 2008, 12:04 PM
xkissesx
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.
• May 14th 2008, 12:31 PM
flyingsquirrel
Hi
Quote:

Originally Posted by xkissesx
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 $V$.

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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 $a\times b\perp b$)
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b) show that the 3 vectors in part a are coplanar
How can one define a plane with a dot and a vector ?
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3) prove that (a-b)x(a+b) = 2(axb)
Cross product distributes over addition : $u\times(v+w)=u\times v+u\times w$