Answer to Question #298778 in Analytic Geometry for peter

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

$$\overrightarrow{AB}=5\vec a+4\vec b+3\vec c-(3\vec a-7\vec b-7\vec c)$$

$$=2\vec a+11\vec b+10\vec c$$

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

$$\cos \alpha=\dfrac{2}{15}$$

$$\cos \beta=\dfrac{11}{15}$$

$$\cos \gamma=\dfrac{10}{15}$$