# Math Help - vector questions

1. ## vector questions

If 1) $a=i+j+k \ \mbox{find}\ b \ \mbox{if}\ a\cdot\mbox{b}=8\ \mbox{and}\ a\times\mbox{b}=6i-7j+k$

2)If a = i + j + k, explain why it is not possible that a x b = i - j + 2k. Show that if a x b = xi + yj + zk, then x + y +z = 0

THanks

2. Originally Posted by ashes
If 1) $a=i+j+k \ \mbox{find}\ b \ \mbox{if}\ a\cdot\mbox{b}=8\ \mbox{and}\ a\times\mbox{b}=6i-7j+k$

...
Let b = (x, y, z) then you know:

[1]: (1, 1, 1) * (x, y, z) = x + y + z = 8

[2]: $(1, 1, 1) \times (x, y, z) = (6, -7, 1)$

#[2] will yield: (z-y, x-z, y-x) = (6, -7, 1)

You'll get a system of simultaneous equations:

$\left|\begin{array}{lcr}z-y&=&6 \\ x-z&=& -7 \\y-x&=&1 \\x+y+z&=&8\end{array} \right.$

Solve for (x, y, z). I've got: (x, y, z) = (0, 1, 7)