Originally Posted by

**Paymemoney** Hi

I need help on the following:

Find the value of t that makes the angle between two vectors a=(3,1,0) and b(t,0,1) equal to 45 degrees.

This is what i have done:

$\displaystyle a \cdot b = ab cos\theta$

$\displaystyle \color{red}{\frac{a \cdot b}{ab} = 45}$

$\displaystyle \frac{3t}{\sqrt{10}\sqrt{t^2+1}} = 45$

$\displaystyle 45\sqrt{10(t^2+1)} = 3t$

$\displaystyle \sqrt{10t^2 + 10} = \frac{3t}{45}$

$\displaystyle 10t^2 + 10 = \frac{t^2}{15^2}$

$\displaystyle 10t^2 + 10 = \frac{t^2}{225}$

$\displaystyle 225(10t^2 + 10) = t^2$

$\displaystyle 2250t^2 + 2250 = t^2$

$\displaystyle 2249t^2 = 2250$

$\displaystyle t=\sqrt{\frac{2250}{2249}}$

$\displaystyle t=1.00$

However the answer is$\displaystyle \frac{\sqrt{5}}{2}$.

P.S