Question #291529

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


1
Expert's answer
2022-01-30T15:19:27-0500

Solution:


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


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



cos(ϕ)=(abab)=(52(10(5)))=1cos(\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).


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


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