NCERT Exemplar Solutions
Class 11 - Mathematics - Chapter : INTRODUCTION TO THREE DIMENSIONAL GEOMETRY
Objective Type Question

Choose the correct answer from the given four options:

Question.  22

The distance of point P(3, 4, 5) from the yz-plane is

(a)

3 units

(b)

4 units

(c)

5 units

(d)

550

Question.  23

What is the length of foot of perpendicular drawn from the point P(3, 4, 5) on y-axis

(a)

\(\sqrt{41}\)

(b)

\(\sqrt{34}\)

(c)

5

(d)

none of these

Question.  24

Distance of the point (3, 4, 5) from the origin (0, 0, 0) is

(a)

\(\sqrt{50}\)

(b)

3

(c)

4

(d)

5

Question.  25

If the distance between the points \((a,0,1)\) and \((0,1,2)\) is \(\sqrt{27}\), then the value of \(a\) is

(a)

5

(b)

\(\pm 5\)

(c)

-5

(d)

none of these

Question.  26

\(x\)-axis is the intersection of two planes

(a)

xy and xz

(b)

yz and zx

(c)

xy and yz

(d)

none of these

Question.  27

Equation of y-axis is considered as

(a)

\(x = 0,\; y = 0\)

(b)

\(y = 0,\; z = 0\)

(c)

\(z = 0,\; x = 0\)

(d)

none of these

Question.  28

The point \((-2, -3, -4)\) lies in the

(a)

First octant

(b)

Seventh octant

(c)

Second octant

(d)

Eighth octant

Question.  29

A plane is parallel to yz-plane so it is perpendicular to :

(a)

x-axis

(b)

y-axis

(c)

z-axis

(d)

none of these

Question.  30

The locus of a point for which \(y = 0,\; z = 0\) is

(a)

equation of x-axis

(b)

equation of y-axis

(c)

equation of z-axis

(d)

none of these

Question.  31

The locus of a point for which \(x = 0\) is

(a)

xy-plane

(b)

yz-plane

(c)

zx-plane

(d)

none of these

Question.  32

If a parallelepiped is formed by planes drawn through the points \((5,8,10)\) and \((3,6,8)\) parallel to the coordinate planes, then the length of diagonal of the parallelepiped is

(a)

\(2\sqrt{3}\)

(b)

\(3\sqrt{2}\)

(c)

\(\sqrt{2}\)

(d)

\(\sqrt{3}\)

Question.  33

\(L\) is the foot of the perpendicular drawn from a point \(P(3,4,5)\) on the xy-plane. The coordinates of point \(L\) are

(a)

(3, 0, 0)

(b)

(0, 4, 5)

(c)

(3, 0, 5)

(d)

none of these

Question.  34

\(L\) is the foot of the perpendicular drawn from the point \((3,4,5)\) on x-axis. The coordinates of \(L\) are

(a)

(3, 0, 0)

(b)

(0, 4, 0)

(c)

(0, 0, 5)

(d)

none of these

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