Question

If lines `(x - 1)/2 = (y + 1)/3 = (z - 1)/4` and x – 3 = `(y - k)/2` = z intersect then the value of k is ______.

Options

• `9/2`

• `1/2`

• `5/2`

• `7/2`

Answer 1

If lines `(x - 1)/2 = (y + 1)/3 = (z - 1)/4` and x – 3 = `(y - k)/2` = z intersect then the value of k is `underlinebb(9/2)`.

Explanation:

Points on the given lines are respectively (1, –1, 1) and (3, k, 0) and their direction ratios are respectively 2, 3, 4 and 1, 2, 1

Since lines intersect, then lines are coplanar

∴ `|(x_2 - x_1, y_2 - y_1, z_2 - z_1),(a_1, b_1, c_1),(a_2, b_2, c_2)|` = 0

∴ `|(2, k + 1, -1),(2, 3, 4),(1, 2, 1)|` = 0

∴ 2(–5) – (k + 1)(–2) – 1(1) = 0

– 11 + 2k + 2 = 0

k = `9/2`