First slide

Planes in 3D

Question

Let the equations of a line and a plane be $\frac{x + 3}{2} = \frac{y - 4}{3} = \frac{z + 5}{2} and 4 x - 2 y - z = 1, respectively, then$

Moderate

A

the line is parallel to the plane
B

the line is perpendicular to the plane
C

the line lies in the plane
D

none of these

Solution

4(2) - 2(3) - 1(2) = 0
Also, point (-3, 4, -5) does not lie on the plane.
Therefore, the line is parallel to the plane.

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