3D Geometry 3 Question 49

####49. 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

(2003, 1M)

(a) 7

(b) -7

(c) No real value

(d) 4

Objective Question II

(One or more than one correct option)

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Answer:

Correct Answer: 49. (a)

Solution:

  1. Given equation of straight line

$ \frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2} $

Since, the line lies in the plane $2 x-4 y+z=7$.

Hence, point $(4,2, k)$ must satisfy the plane.

$ \Rightarrow \quad 8-8+k=7 \Rightarrow k=7 $



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