Question

Find the distance between the following parallel lines: r→ = (2î + ĵ − k̂) + λ(î + ĵ − k̂) r→ = (î − 2ĵ + k̂) + μ(î + ĵ − k̂)

Find the coordinates of the point where the line through the points (−1, 1, −8) and (5, −2, 10) crosses the ZX-plane.

Find the distance between the following parallel lines: r = (2î + ĵ − k̂) + λ(î + ĵ − k̂) and r = (î − 2ĵ + k̂) + μ(î + ĵ − k̂)

Two vertices of the parallelogram ABCD are given as A(–1, 2, 1) and B(1, –2, 5). If the equation of the line passing through C and D is (x – 4)/1 = (y + 7)/(– 2) = (z – 8)/2, then find the distance between sides AB and CD. Hence, find the area of parallelogram ABCD.