The plane (2 x - 2 y - 3 z - 14 = 0) and the line joining... | MATH - LINE AND PLANE | SolveeIt

The plane $2 x - 2 y - 3 z - 14 = 0$ and the line joining (1, 2, 4) and (3, 3, 0) intersect at

(5, 2, 0)

(5, 4, -4)

(-3, -1, -6)

(10, -15, 12)

Answer

(5, 4, -4)

Explanation

Any point on the given line is $( 1 + 2 t , 2 + t , 4 - 4 t )$

This lies in the given plane;

i.e. $2 ( 1 + 2 t ) - 2 ( 2 + t ) - 3 ( 4 - 4 t ) - 14 = 0$

(i.e.,) $4 t - 2 t + 12 t + 2 - 4 - 12 - 14 = 0$

(i.e.) $14 t - 28 = 0$

$\therefore$ t = 2

∴ Intersection point is (5, 4, -4)

Question: The plane \(2 x - 2 y - 3 z - 14 = 0\) and the line joining (1, 2, 4) and (3, 3, 0) intersect at...