The distance between the line $$\vec r = 2\hat i - 2\hat j + 3\hat k + \lambda \left( {i - j + 4k} \right)$$ and the plane $$\vec r.\left( {\hat i + 5\hat j + \hat k} \right) = 5$$ is :
A.
$$\frac{{10}}{9}$$
B.
$$\frac{{10}}{{3\sqrt 3 }}$$
C.
$$\frac{3}{{10}}$$
D.
$$\frac{{10}}{3}$$
Answer :
$$\frac{{10}}{{3\sqrt 3 }}$$
Solution :
A point on line is $$\left( {2,\, - 2,\,3} \right)$$ its perpendicular distance from the plane $$x+5y+z-5=0$$ is
$$ = \left| {\frac{{2 - 10 + 3 - 5}}{{\sqrt {1 + 25 + 1} }}} \right| = \frac{{10}}{{3\sqrt 3 }}$$
Releted MCQ Question on Geometry >> Three Dimensional Geometry
Releted Question 1
The value of $$k$$ such that $$\frac{{x - 4}}{1} = \frac{{y - 2}}{1} = \frac{{z - k}}{2}$$ lies in the plane $$2x - 4y + z = 7,$$ is :
If the lines $$\frac{{x - 1}}{2} = \frac{{y + 1}}{3} = \frac{{z - 1}}{4}$$ and $$\frac{{x - 3}}{1} = \frac{{y - k}}{2} = \frac{z}{1}$$ intersect, then the value of $$k$$ is :
A plane which is perpendicular to two planes $$2x - 2y + z = 0$$ and $$x - y + 2z = 4,$$ passes through $$\left( {1,\, - 2,\,1} \right).$$ The distance of the plane from the point $$\left( {1,\,2,\,2} \right)$$ is :
Let $$P\left( {3,\,2,\,6} \right)$$ be a point in space and $$Q$$ be a point on the line $$\vec r = \left( {\hat i - \hat j + 2\hat k} \right) + \mu \left( { - 3\hat i + \hat j + 5\hat k} \right)$$
Then the value of $$\mu $$ for which the vector $$\overrightarrow {PQ} $$ is parallel to the plane $$x-4y+3z=1$$ is :