Test Details

Introduction to Three Dimensional Geometry

Feb 09, 8:00 PM

45 minutes

Feb 09, 8:45 PM

25.0 marks

MCQ

20 questions

rahul panday

Class Details

Maths

Class -11

Maths

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Question Text

Question 1 :
The ratio in which $xy-$plane divides the line joining the points $(1, 0, -3)$ and $(1, -5, 7)$ is given by

Question 2 :
The coordinate of any point, which lies in $xy$ plane , is

Question 3 :
If $A= (1, 2, 3), B = (2, 3, 4)$ and $AB$ is produced upto $C$ such that $2AB = BC$, then $C =$

Question 4 :
A point on XOZ-plane divides the join of $(5, -3, -2)$ and $(1, 2, -2)$ at

Question 5 :
State the following statement is True or False If two distinct lines are intersecting each other in a plane then they cannot have more than one point in common.

Question 7 :
If the $zx$-plane divides the line segment joining $(1,-1,5)$ and $(2,3,4)$ in the ratio $p:1$, then $p+1=$

Question 10 :
The points (2, 5) and (5, 1) are the two opposite vertices of a rectangle. If the other two vertices are points on the straight line $y = 2x + k$, then the value of k is

Question 11 :
$A(3, 2, 0), B(5, 3, 2), C(-9, 6, -3)$ are three points forming a triangle. If $AD$, the bisector of $\angle BAC$ meets $BC$ in $D$ then coordinates of $D$ are

Question 12 :
In three dimensions, the coordinate axes of a rectangular cartesian coordinate system are

Question 14 :
Plane $ax + by + cz = 1$ intersect axes in $A, B, C$ respectively. If $G\left (\dfrac {1}{6}, -\dfrac {1}{3}, 1\right )$ is a centroid of $\triangle ABC$ then $a + b + 3c =$ _________.

Question 16 :
The equation of plane passing through $(-1,0,-1)$ parallel to $xz$ plane is

Question 17 :
The ratio in which the plane $\displaystyle \bar {r} .(\bar {i} - 2 \bar {j} + 3 \bar {k}) = 17$ divides the line joining the points $\displaystyle -2 \bar {i} + 4 \bar {j} + 7 \bar {k} $ and $\displaystyle 3 \bar {i} - 5 \bar {j} + 8 \bar {k}$ is

Question 18 :
The xy-plane divides the line joining the points (-1, 3, 4) and (2,-5,6).

Question 19 :
An equation of sphere with centre at origin and radius $r$ can be represented as

Question 20 :
The foot of the perpendicular from the point $A(7, 14, 5)$ to the plane $2x+4y-z=2$ is?

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