A vector of magnitude 2 along a bisector of the angle between the two vectors 2i^� −2j^� +k^� and i^� +2j^� −2k^� is _


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Question Number 115258 by bobhans last updated on 24/Sep/20

$A v e c t o r o f m a g n i t u d e 2 a l o n g a b i s e c t o r$ $o f t h e a n g l e b e t w e e n t h e t w o v e c t o r s$ $2 \hat{i} - 2 \hat{j} + \hat{k} a n d \hat{i} + 2 \hat{j} - 2 \hat{k} i s__$
	Answered by bemath last updated on 24/Sep/20

	$l e t \vec{a} = (2, - 2, 1) & \vec{b} = (1, 2, - 2)$ $\Rightarrow v e c t o r a l o n g b i s e c t o r i s g i v e n$ $b y \frac{\vec{a}}{∣ \vec{a} ∣} \pm \frac{\vec{b}}{∣ \vec{b} ∣} = \frac{(2, - 2, 1)}{3} \pm \frac{(1, 2, - 2)}{3}$ $= (1, 0, - \frac{1}{3}) o r (\frac{1}{3}, - \frac{4}{3}, 1)$ $R e q u i r e d v e c t o r a r e$ $(i) 2 . \frac{(1, 0, - \frac{1}{3})}{\sqrt{1 + \frac{1}{9}}} = \frac{(6, 0, - 2)}{\sqrt{10}}$ $(i i) 2 . \frac{(\frac{1}{3}, - \frac{4}{3}, 1)}{\sqrt{\frac{26}{9}}} = \frac{(2, - 8, 6)}{\sqrt{26}}$
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