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.

2. Hi
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.
$\displaystyle V=\begin{pmatrix}x\\y\\z\end{pmatrix}$

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

2) vector u is give as u= (1, -2, 1)
a) determine 3 different non-collinear vectors perpindicular to u.
For any two vectors $\displaystyle a$ and $\displaystyle b$, $\displaystyle a\times b\perp a$. (and $\displaystyle a\times b\perp b$)
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 : $\displaystyle u\times(v+w)=u\times v+u\times w$