Find the acute angle between the lines whose direction ratios are proportional to 2:3:6 and 1:2:2.
Given that the direction ratios of the lines are proportional to 2:3:6 and 1:2:2.
Let us denote the lines in the form of vectors as A and B.
Let’s write the vectors:
⇒ A = 2i + 3j + 6k
⇒ B = 1i + 2j + 2k
We know that the angle between the vectors a1i + b1j + c1k and a2i + b2j + c2k is given by:
⇒
Let’s assume the angle between the vectors A and B be ,
Using the given formula we find the value of .
⇒
⇒
⇒
⇒
⇒
The acute angle between the two vectors is given by .