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 L₂ : r⃗ = î + (2μ + 1)ĵ − (μ + 2)k̂.

The Cartesian equation of the line passing through the point (1, -3, 2) and parallel to the line : r = (2 + λ)i + λj + (2λ - 1)k is

Find the point of intersection of the lines r→ = î – ĵ + 6k̂ + λ(3î – k̂), and r→ = –3ĵ + 3k̂ + μ(î + 2ĵ – k̂). Also, find the vector equation of the line passing through the point of intersection of the given lines and perpendicular to both the lines.