Question

The angle between the diagonals of the parallelogram formed by the points $(1, 2, 3), (-1, -2, -1), (2, 3, 2), (4, 7, 6)$ is

• A. $\cos^{-1} (7)$
• B. $\cos^{-1} \left(\frac{7}{\sqrt{155}}\right)$
• C. $\cos^{-1} \left(\frac{7}{\sqrt{465}}\right)$
• D. $\cos^{-1} \left(\frac{7}{465}\right)$

Answer 1

Answer: (C)

D.r's of AC = (1,1,-1), D.r's of BD = (5,9,7)
$\cos \theta \frac{5+9-7}{\sqrt{3} . \sqrt{155} } \Rightarrow \theta = \cos^{-1} \left(\frac{7}{\sqrt{465}}\right) $