Question

The image of the point (1, 6, 3) in the line `x/1 = (y - 1)/2 = (z - 2)/3` is ______ 

Options

• (1, 0, 7)

• (7, 0, 1)

• (2, 7, 0)

• (-1, -6, -3)

Answer 1

The image of the point (1, 6, 3) in the line `x/1 = (y - 1)/2 = (z - 2)/3` is (1, 0, 7).

Explanation:

 Let `x/1 = (y - 1)/2 = (z - 2)/3 = lambda`

Any general point on this line is

M ≡ (λ, 2λ + 1, 3λ + 2)

Let A ≡ (1, 6, 3)

d.r.s. of AM are λ - 1, 2λ - 5, 3λ - 1

Since AM is perpendicular to the given line,

1(λ - 1) + 2(2λ - 5) + 3(3λ - 1) = 0

⇒ 14λ = 14

⇒ λ = 1

∴ M = (1, 3, 5)

Now, M is the midpoint of AB.

∴ `((1 + x_1)/2, (6 + y_1)/2, (3 + z_1)/2) = (1, 3, 5)`

⇒ x₁ = 1, y₁ = 0, z₁ = 7