Michael Maggard

2021-12-15

Vector Dot Product Learning Goal: To understand the rules for computing dot products. Let vectors $B=\left(-3,0,1\right),C=\left(-1,-1,2\right)$
Dot product of two vectors multiplied by constants Calculate $2\stackrel{―}{B}\cdot 3\stackrel{―}{C}$. Express your answer numerically. $2\stackrel{―}{B}\cdot 3\stackrel{―}{C}=$

vicki331g8

Expert

Dot product of two vectors multiplied by constants:
$2\stackrel{―}{B}\cdot 3\stackrel{―}{C}=2\left(-3,0,1\right)\cdot 3\left(-1,-1,2\right)$
$\therefore 2\stackrel{―}{B}\cdot 3\stackrel{―}{C}=\left(-6,0,2\right)\cdot \left(-3,-3,6\right)$
$\therefore 2\stackrel{―}{B}\cdot 3\stackrel{―}{C}=\left(-6×\left(-3\right)\right)+\left(0×\left(-3\right)\right)+\left(2×6\right)$
$\therefore 2\stackrel{―}{B}\cdot 3\stackrel{―}{C}=18+0+12$
$\therefore 2\stackrel{―}{B}\cdot 3\stackrel{―}{C}=30$

Papilys3q

Expert

Is there a more shortly solution?

nick1337

Expert

Here:
The dot product of vectors $2\stackrel{―}{B}\cdot 3\stackrel{―}{C}$ is,
Here, p and q are constans, ${C}_{x},{C}_{y},{C}_{z}$ are the $x,y,z$ components of vector $\stackrel{―}{C},$
Substitute 2 for p, 3 for q, -1 for ${C}_{x}$, -1 for C_x${C}_{y}$, 2 for ${C}_{z}$, -3 for ${B}_{x}$, 1 for ${B}_{z}$. The dot product of the vectors is,
$2\stackrel{―}{B}\cdot 3\stackrel{―}{C}=30$

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