Question

Find the coordinates of the point where the line through the points A (3, 4, 1) and B (5, 1, 6) crosses the plane determined by the points P (2, 1, 2), Q (3, 1, 0) and R (4, –2, 1).

Answer 1

The line through A (3, 4, 1) and B(5, 1, 6) is given by

The equation of plane determined by the points P(2, 1, 2), Q(3, 1, 0) and R(4, -2, 1) is given by,

Let S \((\alpha, \beta, \gamma)\) be intersecting point of line (I) and plane (II)

\(\because\) S \((\alpha, \beta, \gamma)\) lie on line (I)

\(\because\) S \((\alpha, \beta, \gamma)\) also lie on plane (II)

\(\therefore\) Required point of intersection \(= \big(\frac{5}{3}, 6, -\frac{7}{3} \big).\)