Test Details

Line and Plane

Jan 29, 9:00 PM

720 minutes

Feb 02, 11:00 PM

20.0 marks

MCQ

13 questions

Rahul Gayke

Teacher

Class Details

Mathematics

XII Mathematics

Mathematics

Shriram Vidyalaya, Dhorjalgaon SYJC Mathematics

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Question Text

Question 2 :
The shortest distance between the skew lines $\frac { x - 3 } { - 1 } = \frac { y - 4 } { 2 } = \frac { z + 2 } { 1 } , \frac { x - 1 } { 1 } = \frac { y + 7 } { 3 } = \frac { z + 2 } { 2 }$ is

Question 3 :
The equation of the plane passing through $(a,b,c)$ and parallel to the plane $r.(\hat{i}+\hat{j}+\hat{k})=2$ is,

Question 4 :
If $P$ is a point on the line passing through the point $A$ with position vector $2\overline{i}+\overline{j}-3\overline{k}$ and parallel to $\overline{i}+2\overline{j}+\overline{k}$ such that $AP=2\sqrt{6}$ then the position vector of $P$ is

Question 5 :
Find vector equation for the line passing through the points $3\overline i+4\overline j-7\overline k,\overline i-\overline j+6\overline k$.

Question 7 :
A line passed through the point $A(6,2,2)$ and is parallel to the vector $(1,-2,2)$. Another line passes through the point $B(-4,0,-1)$ and is parallel to the vector $(3,-2,-2)$. The shortest distance between these two lines is

Question 8 :
Find the shortest distance between the lines $\displaystyle \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\displaystyle \frac{x - 2}{3} = \frac{y - 4}{4} = \frac{z - 5}{5}$.

Question 9 :
The distance between the lines $\displaystyle \frac {x-4}{2}=\frac {y+1}{-3}=\frac {z}{6}$ and $\displaystyle \frac {x}{-1}=\frac {y-1}{\dfrac {3}{2}}=\frac {z+1}{-3}$ is

Question 10 :
If $(2, 3, -1)$ is the foot of the perpendicular from $(4, 2, 1)$ to a plane, then the equation of that plane is $ax+by+cz=d$. Then $a+d$ is

Question 12 :
The length of the shortest distance between the lines $r = 3 i + 8 j + 7 k + \lambda ( 1 - 2 j + k )$ and $r = - i - j - k + \mu ( 7 i - 6 j + k )$ is

Question 13 :
Find the values of p so the line $\dfrac{1-x}{3}=\dfrac{7y-14}{2p}=\dfrac{z-3}{2}$ and $\dfrac{7-7x}{3p}=\dfrac{y-5}{1}=\dfrac{6-z}{5}$ are at right angles.

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