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. 21
• C. 22
• D. 26

Answer 1

The correct option is A 20

It is easy to see $AB=i-2j+4k;$
$AC=2i-3j+3k$
Therefore
$AB\cdot AC=20$
$AB\cdot AB=21,$
$AC\cdot AC=22$
Thus $\cos \theta =\frac{AB\cdot AC}{\left|AB\right|\left|AC\right|}=\frac{20}{\sqrt{462}}$
So $\sqrt{462}cos\theta$ $=20$