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:
- 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 $
