Question

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.

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.