First slide

Planes in 3D

Question

The coordinates of the point where the line through $(3, - 4, - 5)$ and $(2, - 3, 1)$ crosses the plane $2 x + y + z = 7$ is

Moderate

A

$(- 1, 2, 7)$
B

$(1, - 2, 7)$
C

$(1, 2, 7)$
D

$(- 1, - 2, 7)$

Solution

Equation of line through (3,-4,-5) and (2,-3,1) is $\frac{x - 3}{- 1} = \frac{y + 4}{1} = \frac{z + 5}{6}$ =t
point (3-t,-4+t,-5+6t) subtute in given plane
now solve this line and the given plane

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