Show that two nonzero vectors v1 and v2 are orthogonalif and only if their direction

Chapter 11, Problem 20

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Show that two nonzero vectors $v_{1}$ and $v_{2}$ are orthogonal if and only if their direction cosines satisfy

$\cos \alpha_{1} \cos \alpha_{2}+\cos \beta_{1}^{-} \cos \beta_{2}+\cos \gamma_{1} \cos \gamma_{2}=0$

Equation Transcription:

${v}_{1}$

${v}_{2}$

$cos\ {\alpha{}}_{1}cos{\ \alpha{}}_{2}+cos{\ {\beta{}}^{-}}_{1}cos\ {\beta{}}_{2}+cos\ {\gamma{}}_{1}cos{\ \gamma{}}_{2}=0$

Text Transcription:

v_1

v_2

cos⁡ alpha_1cos ⁡alpha_2+cos beta⁡‾_1 cos⁡ beta_2+cos⁡ gamma_1cos⁡ gamma_2=0

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