#### Question

Find the coordinates of the point where the line through (3, −4, −5) and (2, − 3, 1) crosses the plane 2*x* + *y *+ *z* = 7).

#### Solution

It is known that the equation of the line through the points, (*x*_{1}, *y*_{1}, *z*_{1}) and (*x*_{2}, *y*_{2}, *z*_{2}), is

Therefore, any point on the line is of the form (3 − *k*, *k* − 4, 6*k* − 5).

This point lies on the plane, 2*x* + *y* + *z* = 7

∴ 2 (3 − *k*) + (*k* − 4) + (6*k* − 5) = 7

`=> 5k - 3 =7`

`=> k = 2`

Hence, the coordinates of the required point are (3 − 2, 2 − 4, 6 × 2 − 5) i.e.,

(1, −2, 7).

Is there an error in this question or solution?

Solution Find the Coordinates of the Point Where the Line Through (3, −4, −5) and (2, − 3, 1) Crosses the Plane 2x + Y + Z = 7). Concept: Plane - Equation of a Plane in Normal Form.