Answer to Question #305213 in Analytic Geometry for asher

Question

If the position vector of A and B are 3

−→a − 7

−→b − 7

−→c and 5

−→a + 4

−→b + 3−→c , nd −→AB

and determine its magnitude and direction cosines.

Answer 1

$$\overrightarrow{AB}=(5-3, 4-(-7), 3-(-7))$$

$$\overrightarrow{AB}=(2,11,10)$$

$$|\overrightarrow{AB}|=\sqrt{2^2+11^2+10^2}=15$$

Direction cosines are $\bigg(\dfrac{2}{15}, \dfrac{11}{15}, \dfrac{2}{3}\bigg).$