3D Geometry 3 Question 60
60. Consider the planes $3 x-6 y-2 z=15$ and $2 x+y-2 z=5$.
Statement I The parametric equations of the line of intersection of the given planes are $x=3+14 t$, $y=1+2 t, z=15 t$.
Statement II The vectors $14 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+15 \hat{\mathbf{k}}$ is parallel to the line of intersection of the given planes.
$(2007,3 M)$
Match the Columns
Match the conditions/expressions in Column I with values statements in Column II.
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Answer:
Correct Answer: 60. (d)
Solution:
- Given planes are $3 x-6 y-2 z=15$ and $2 x+y-2 z=5$.
For $z=0$, we get $x=3, y=-1$
Since, direction ratios of planes are
$ <3,-6,-2>\text { and }<2,1,-2> $
Then the DR’s of line of intersection of planes is $<14,2,15>$ and line is
$ \begin{aligned} \frac{x-3}{14} & =\frac{y+1}{2}=\frac{z-0}{15}=\lambda \\ & \\ \Rightarrow \quad x=14 \lambda+3, y & =2 \lambda-1, z=15 \lambda \end{aligned} $
Hence, Statement I is false.
But Statement II is true.
