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Question
Find the coordinates of the point where the line through (3, −4, −5) and (2, − 3, 1) crosses the plane 2x + y + z = 7).
Solution
It is known that the equation of the line through the points, (x1, y1, z1) and (x2, y2, z2), is
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).
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