eVector

Example Given ${\bf A} = (-1,2,3), {\bf B} = (0,-3,2)$ ,　Find the following values. 1. $3{\bf B} - 2{\bf A}$
2. Angle $\theta$ between A and B

Answer 1. $3{\bf B} - 2{\bf A} = 3(0,-3,2) -2(-1,2,3) = (2,-13,0)$ . 2. Since ${\bf A}\cdot {\bf B} = \vert{\bf A}\vert\vert{\bf B}\vert\cos{\theta}$ , we have

$\displaystyle \cos{\theta}$	$\displaystyle =$	$\displaystyle \frac{{\bf A}\cdot {\bf B}}{\vert{\bf A}\vert\vert{\bf B}\vert}$
	$\displaystyle =$	$\displaystyle \frac{0}{\sqrt{1+4+9}\sqrt{0+9+4}} = 0$

Thus the angle $\theta = \frac{\pi}{2}$ . We note that $A$

and

are diagonal.

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