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

The value of $m$, such that $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-m}{2}$ lies in the plane $2 x-4 y+z=7$, is
  1. 7
  2. -7
  3. no real value
  4. 4

Solution

The line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-\mathrm{k}}{2}$ lies in the plane $2 x-4 y+z=7$. $\therefore \quad$ the point $(4,2, k)$ lies on the line and hence lies in the plane $\begin{array}{ll} \therefore \quad & 2(4)-4(2)+k=7 \\ & \Rightarrow k=7 \end{array}$

Asked in: MHT CET 2024 (09 May Shift 1)

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