Hello saeros Originally Posted by
saeros I understand, but then I get to a equation I obviously can't solve
!
It's like that:
$\displaystyle
5k - \sqrt{34\cdot(4+k^2)} + 6 = 0
$
I guess I'm not wrong at this point.. but I have no clue how to get
k out of it. Any clues please?
I assume it's part (b) that you're stuck with. So here it is:$\displaystyle \textbf{p}.\textbf{q}=|\textbf{p}||\textbf{q}|\cos \phi$
$\displaystyle \Rightarrow 5k+6 = \sqrt{34(4+k^2)}.\frac{1}{\sqrt2}$, when $\displaystyle \phi = 45^o$
Square both sides:$\displaystyle \Rightarrow 25k^2+60k+36 = 17(4+k^2)$$\displaystyle =68+17k^2$
$\displaystyle \Rightarrow 8k^2 + 60k -32 = 0$
$\displaystyle \Rightarrow 2k^2+15k-8=0$
$\displaystyle \Rightarrow (2k-1)(k+8)=0$
$\displaystyle \Rightarrow k = \tfrac12,\;-8$
When you substitute back in the original equation, the negative root is invalid. So the answer is:
$\displaystyle k = \tfrac12$
Grandad