JEE Advance - Mathematics (2009 - Paper 2 Offline - No. 5)
A line with positive direction cosines passes through the point P(2, $$-$$1, 2) and makes equal angles with the coordinate axes. The line meets the plane $$2x + y + z = 9$$ at point Q. The length of the line segment PQ equals
$$1$$
$${\sqrt 2 }$$
$${\sqrt 3 }$$
$$2$$
Explanation
The D.C. of the line are $${1 \over {\sqrt 3 }},{1 \over {\sqrt 3 }},{1 \over {\sqrt 3 }}$$.
We find that any point on the line at a distance $$t$$ from $$P(2, - 1,2)$$ is
$$\left( {2 + {t \over {\sqrt 3 }}, - 1 + {t \over {\sqrt 3 }},2 + {t \over {\sqrt 3 }}} \right)$$ which lies on $$2x + y + z = 9 $$
$$\Rightarrow t = \sqrt 3 $$.
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