Question

The angle between the lines 2x = 3y = −z and 6x = −y = −4z is

Find the angle between the following two lines: →r = 2î − 5ĵ + k̂ + λ(3î + 2ĵ + 6k̂); →r = 7î − 6k̂ + μ(î + 2ĵ + 2k̂)

If l₁, m₁, n₁ and l₂, m₂, n₂ are direction cosines of lines L₁ and L₂ respectively and θ is the acute angle between them, then :

(a) If the lines (x – 3)/1 = (1 – y)/1 = (z + 2)/p and (2 – x)/3 = (y + 1)/5 = (z + 56)/(2p) are perpendicular to each other, then find the value(s) of p.