Question

If the lines (x – 1)/(–3) = (y – 2)/(2k) = (z – 3)/2 and (x – 1)/(3k) = (y – 1)/1 = (z – 6)/(–7) are perpendicular to each other, find the value of k and hence write the vector equation of a line perpendicular to these two lines and passing through the point (3, –4, 7).

The Cartesian equation of the line passing through the point (1, −3, 2) and parallel to the line r⃗ = (2 + λ)î + λĵ + (2λ − 1)k̂ is :

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 L₂ : r⃗ = î + (2μ + 1)ĵ − (μ + 2)k̂.