A) \[\frac{-1}{2}\]
B) \[\frac{19}{4}\]
C) \[\frac{-19}{4}\]
D) \[\frac{25}{7}\]
Correct Answer: D
Solution :
The equation of line passing through the point \[A(3,-1,4)\] and \[B(-4,2,1)\]. \[\frac{x-{{x}_{1}}}{{{x}_{2}}-{{x}_{1}}}=\frac{y-{{y}_{1}}}{{{y}_{2}}-{{y}_{1}}}=\frac{z-{{z}_{1}}}{{{z}_{2}}-{{z}_{1}}}\] \[\Rightarrow \] \[\frac{x-3}{-4-3}=\frac{y+1}{2+1}=\frac{z-4}{1-4}\] \[\Rightarrow \] \[\frac{x-3}{-7}=\frac{y+1}{3}=\frac{z-4}{-3}\] Since, the point \[P(2,y,z)\] passing through the above line, then \[\Rightarrow \] \[\frac{2-3}{-7}=\frac{y+1}{3}=\frac{z-4}{-3}\] \[\Rightarrow \] \[\frac{y+1}{3}=\frac{z-4}{-3}=\frac{1}{7}\] \[\Rightarrow \] \[y=\frac{3}{7}-1\] and \[z=-\frac{3}{7}+4\] \[\Rightarrow \] \[y=-\frac{4}{7}\] and \[z=\frac{25}{7}\]
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