I've been working on two questions both of which have been giving me trouble. The first states:

Determine "k" given two vectors and the angle between them.

vectors a=(1,1) and b=(0,k) with and angle of 45 degrees.

I was using the dot product to solve with with

a.b= lal lbl cos45

0= (sqrt 2) + kcos45

-(sqrt 2)/cos 45 =k

k=2

if anyone could tell me if I'm right that be fantastic

The second question is similar:

Find the value of "p" if the vectors r=(p,p,1) and s+(p,-2,-3) are perpendicular to each other

again i used the dot product and got

0=lal lbl cos90

0= (p)(p) +(p)(-2)+(-1)(3)

0= (p^2) -2p -3

3= (p^2) -2p

this is where I get stuck so if anyone could help me out it would be much appreciated thank you