Question

If $\theta$ is the angle between the lines $AB,AC$ where $A,B,C$ are the three points with coordinates $(1,2,-1);(2,0,3);(3,-1,2)$ respectively, then $\sqrt{462}\cos \theta$ is equal to

• A. $20$
• B. $40$
• C. $60$
• D. $120$

Answer 1

Answer: (A)

$20$

We get

$\overline{AB}=\overline{i}-2\overline{j}+4\overline{k}$
$\overline{AC}=2\overline{i}-3\overline{j}+3\overline{k}$

$\cos \theta =\frac{\overline{AB}.\overline{AC}}{|\overline{AB}|\times |\overline{AC}|}$

$\therefore \sqrt{462}\cos \theta =\overline{AB}.\overline{AC}=2+6+12=20$