Question

Find the vector equation of the line passing through the point (2, 3, −5) and making equal angles with the co-ordinate axes.

Find the shortest distance between the lines L₁ & L₂ given below : L₁ : The line passing through (2, -1, 1) and parallel to x/1 = y/1 = z/3, and L₂ : r⃗ = î + (2μ + 1)ĵ - (μ + 2)k̂.

Find the shortest distance between the lines (x – 8)/3 = (y + 9)/(–16) = (z – 10)/7 and (x – 15)/3 = (y – 29)/8 = (z – 5)/(–5).

Find the vector and the Cartesian equations of a line passing through the point (1, 2, −4) and parallel to the line joining the points A(3, 3, −5) and B(1, 0, −11). Hence, find the distance between the two lines.