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The value of k such that (x-4)/1=(y-2)/1...

The value of `k` such that `(x-4)/1=(y-2)/1=(z-k)/2` lies in the plane `2x-4y=z=7` is a. 7 b. -7 c. no real value d. 4

A

7

B

-7

C

no real value

D

4

Text Solution

Verified by Experts

The correct Answer is:
a
As the line `(x-4)/(1)= (y-2)/(1)= (z-k)/(2)` lies in the plane `2x-4y+z=7`, the point `(4, 2, k)` through which it passes must also lie on the given plane, and hence `2xx4-4xx2+k=7` or `k=7`.
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