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-2-is-1-5-i-2j-

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) .