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Introduction to Three Dimensional Geometry

Jan 20, 3:00 PM

60 minutes

Jan 20, 4:00 PM

20.0 marks

MCQ

20 questions

Ranjeet Sharma

I am passionate about my work. my focus is on Conceptual clarity.

Class Details

Maths

Class 11th

Maths

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Question Text

Question 1 :
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 4 :
The distance of origin from the image of (1, 2, 3) in plane x - y + z = 5 is 

Question 5 :
The point equidistant from the points $(0,0,0), (1,0,0), (0,2,0)$ and $(0,0,3)$ is

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

Question 7 :
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 8 :
The x-coordinate of a point on the line joining the points $P(2,2,1)$ and $Q(5,1,-2)$ is $4$. Find its z-coordinate.

Question 10 :
If $A, B$ are the feet of the perpendiculars from $(2, 4, 5)$ to the $x$-axis, $y$-axis respectively, then the distance $AB$ is

Question 11 :
If the extremities of a diagonal of a square are $(1, -2, 3)$ and $(2, -3, 5)$, then area of the square is

Question 13 :
The equation of the set of points which are equidistant from the points $(1, 2, 3)$ and $(3, 2, -1)$.

Question 14 :
The distance between the parallel planes given by the equations, $\vec{r}.(2\hat{i}-2\hat{j}+\hat{k})+3=0$ and $\vec{r}.(4\hat{i}-4\hat{j}+2\hat{k})+5=0$ is-

Question 15 :
The ratio in which the plane $2x+3y-2z+7=0$ divides the line segment joining the points $(-1, 1, 3)$, $(2, 3, 5)$ is

Question 16 :
The point on the line $\frac{x - 2} {1} = \frac{y + 3} {-2} = \frac{z + 5} {-2} $ at a distance of 6 from the point $\left ( 2, -3, -5 \right )$ is

Question 18 :
The distance between (5,1,3) and the line x=3, y=7+t, z=1+t is

Question 19 :
The ratio in which $xy-$plane divides the line joining the points $(1, 0, -3)$ and $(1, -5, 7)$ is given by

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