Given the position vectors v_1 = 2i − 2j and v_2 = 2j, show that the unit vector in the direction of the vector v_1 − v


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Question Number 36091 by Rio Mike last updated on 28/May/18

$Given the position vectors$ $v_{1} = 2 i - 2 j a n d v_{2} = 2 j,$ $show that the unit vector in$ $the direction of the vector$ $v_{1} - v_{2} is \frac{1}{\sqrt{5}} (i - 2 j)$
Commented by prof Abdo imad last updated on 31/May/18

$w e h a v e v_{1} - v_{2} = 2 i - 2 j - 2 j = 2 i - 4 j s o t h e$ $u n i t v r c t o r i n t h e d i r e c t i o n o f v_{1} - v_{2} i s$ $u = \frac{1}{∣∣ v_{1} - v_{2} ∣∣} (v_{1} - v_{2}) = \frac{1}{\sqrt{4 + 16}} (2 i - 4 j)$ $= \frac{1}{2 \sqrt{5}} (2 i - 4 j) = \frac{1}{\sqrt{5}} (i - 2 j) .$
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