It is known that the equation of the line through the points, (x1, y1, z1) and (x2, y2, z2), is
Since the line passes through the points, (3, −4, −5) and (2, −3, 1), its equation is given by,
Therefore, any point on the line is of the form (3 − k, k − 4, 6k − 5).
This point lies on the plane, 2x + y + z = 7
2 (3 − k) + (k − 4) + (6k − 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).
