Answer to Question #291529 in Analytic Geometry for Abc

Question

Find the angle between the vectors √2i + 2j + 2k and i + √2j + √2k.

Answer 1

Solution:

Let $\overrightharpoon{a}=\sqrt{2}i+2j+2k$ and $\overrightharpoon{b}=i+\sqrt{2}j+\sqrt{2}k.$

Now angle between $\overrightharpoon{a}$ and $\overrightharpoon{b}$ be:

$$cos(\phi)=(\frac{\overrightharpoon{a}\overrightharpoon{b}}{|\overrightharpoon{a}||\overrightharpoon{b}|})=(\frac{5\sqrt{2}}{(\sqrt{10}(\sqrt{5}))})=1$$

(in case of complex numbers, we need to take the real part of the dot product).

$\phi = acos (1) = 0 = 0^o$