Determine the value(s) of k such that the angle between the vectors a= (1,1,k) and b=(1,0,1) is 45 degrees.

Answer 1

a dot b = |a| |b|cosØ
(1,1,k) dot (1,0,1) = √(1+1+k^2) √(1+0+1)cos45°
1 + 0 + k = √(k^2 + 2)√2 * 1/√2
1+k = √(k^2+2)
square both sides
1 + 2k + k^2 = k^2 + 2
2k = 1
k = 1/2

check my arithmetic