Question

Direction ratios of lines l₁ and l₂ are <12, – 3, 9> and <4, q, – p> respectively. The values of p and q for which l₁ and l₂ are parallel are respectively :

(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.

(b) Opposite sides of a square are along the lines : r→ = i^ + 2j^ – 4k^ + λ(2i^ + 3j^ + 6k^) r→ = 3i^ + 3j^ – 5k^ + μ(2i^ + 3j^ + 6k^) Find the area of the square if direction ratios of other pair of opposite sides of the square are given by <– 3, 6, p>. Also, find the value of p.

Direction ratios of lines l₁ and l₂ respectively are <1, −2, 3> and <−2, p, −6>. The value of p for which l₁ ∥ l₂, is :