Given-a-cube-ABCD-EFGH-if-is-the-angle-BEH-amp-BEG-find-the-value-of-cos-

Question Number 105356 by bemath last updated on 28/Jul/20

G i v e n a c u b e A B C D . E F G H .

i f α i s t h e a n g l e B E H & B E G,

f i n d t h e v a l u e o f \cos α ?

Answered by john santu last updated on 28/Jul/20

Commented by john santu last updated on 28/Jul/20

w i t h n o r m a l v e c t o r {\vec{n}}_{1} & {\vec{n}}_{2}

{\vec{n}}_{1} = | \begin{matrix} - 2 0 0 \\ 0 2 - 2 \end{matrix} | = (0, - 4, - 4)

{\vec{n}}_{2} = | \begin{matrix} 0 2 - 2 \\ - 2 2 0 \end{matrix} | = (4, 4, 4)

\cos α = \frac{∣ {\vec{n}}_{1} \circ {\vec{n}}_{2} ∣}{∣ {\vec{n}}_{1} ∣ . ∣ {\vec{n}}_{2} ∣} = \frac{32}{4 \sqrt{2} . 4 \sqrt{3}} = \frac{\sqrt{6}}{3}

(J S ♠ ⧫)

Commented by bemath last updated on 28/Jul/20

g r e a t . .

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