Find the angle between the lines and

Question

Philoid · Accepted Answer

We have lines,

We need to find the angle between the lines.

The line is parallel to vector .

Let . Then, we can say that

The line is parallel to vector .

Similarly, let . Then, we can say that

The line is parallel to vector .

If θ is the angle between the lines, then cosine θ is given by

Substituting values of and in the above equation, we get

Here,

…(i)

Also,

…(ii)

Substituting equation (i) and (ii) in cos θ, we get

Thus, the angle between the lines is .