Answer to Question #105886 in Analytic Geometry for Jflows

Question

If α=α1i+α2j+α3keta=\ eta1i+\ eta2j+\ eta3k, thenαdot \etaαdot\ eta is ____?

a.\\(\\alpha_{1}\\beta_{1}+\\alpha_{2}\\beta_{2}+\\alpha_{3}\\beta_{3}\\)
b.\\(\\alpha_{1}\\beta_{1-\\alpha}\\beta_{2-\\alpha}\\beta_{3-\\alpha}\\)
c.\\(\\alpha_{1}\\beta_{1}-\\alpha_{2}\\beta_{2}-\\alpha_{3}\\beta_{3}\\)
d.\\(\\alpha_{1}\\beta_{1}+\\alpha_{2}\\beta_{2}-\\alpha_{3}\\beta_{3}\\)

Answer 1

We are given $\overrightarrow{\alpha}=\alpha_1i+\alpha_2j+\alpha_3k$ and $\overrightarrow{\beta}=\beta_1i+\beta_2j+\beta_3k$

Then the dot product of both vector is $\overrightarrow{\alpha}.\overrightarrow{\beta}$

$\overrightarrow{\alpha}.\overrightarrow{\beta}=\alpha_1\beta_1+\alpha_2\beta_2+\alpha_3\beta_3$