Question

The co-ordinates of the point where the line joining the points (2, –3, 1), (3, –4, –5) cuts the plane 2x + y + z = 7 are ______.

Options

• (2, 1, 0)

• (3, 2, 5)

• (1, –2, 7)

• None of these

Answer 1

The coordinates of the point where the line joining the points (2, –3, 1), (3, –4, –5) cut the plane 2x + y + z = 7 are (1, –2, 7).

Explanation:

Direction ratios of the line

= (x₂ – x₁), (y₂ – y₁), (z₂ – z₁)

= (1, –1, –6)

This line passes through (2, –3, 1).

Then its equation,

`(x - 2)/1 = (y + 3)/(-1) = (z - 1)/(-6)` = r (say)

The coordinates of any point on this line are (r + 2, –r – 3, –6r + 1).

If this point lies on the plane 2x + y + z = 7

Then 2(r + 2) + (–r – 3) + (–6r + 1) = 7

⇒ –5r = 5

⇒ r = –1

The coordinates of the required points are (1, –2, 7).