First slide

Planes in 3D

Question

$The value of k such that \frac{x - 4}{1} = \frac{y - 2}{1} = \frac{z - k}{2} lies in the plane 2 x - 4 y + z = 7 is$

Moderate

A

7
B

-7
C

No real value
D

4

Solution

$As the line \frac{x - 4}{1} = \frac{y - 2}{1} = \frac{z - k}{2} lies in the plane 2 x - 4 y + z = 7$
$the point (4, 2, k) through which it passes must also lie on the given plane, and hence 2 \times 4 - 4 \times 2 + k = 7 or k = 7 .$

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