Commerce Exam  >  Commerce Tests  >  Mathematics (Maths) Class 11  >  Test: Introduction To Three Dimensional Geometry- 1 - Commerce MCQ

Test: Introduction To Three Dimensional Geometry- 1 - Commerce MCQ


Test Description

25 Questions MCQ Test Mathematics (Maths) Class 11 - Test: Introduction To Three Dimensional Geometry- 1

Test: Introduction To Three Dimensional Geometry- 1 for Commerce 2024 is part of Mathematics (Maths) Class 11 preparation. The Test: Introduction To Three Dimensional Geometry- 1 questions and answers have been prepared according to the Commerce exam syllabus.The Test: Introduction To Three Dimensional Geometry- 1 MCQs are made for Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Introduction To Three Dimensional Geometry- 1 below.
Solutions of Test: Introduction To Three Dimensional Geometry- 1 questions in English are available as part of our Mathematics (Maths) Class 11 for Commerce & Test: Introduction To Three Dimensional Geometry- 1 solutions in Hindi for Mathematics (Maths) Class 11 course. Download more important topics, notes, lectures and mock test series for Commerce Exam by signing up for free. Attempt Test: Introduction To Three Dimensional Geometry- 1 | 25 questions in 25 minutes | Mock test for Commerce preparation | Free important questions MCQ to study Mathematics (Maths) Class 11 for Commerce Exam | Download free PDF with solutions
Test: Introduction To Three Dimensional Geometry- 1 - Question 1

The distance of the point (3, 4, 5) from X- axis is 

Detailed Solution for Test: Introduction To Three Dimensional Geometry- 1 - Question 1

x is 3 units to the right from (0, 4, 5)
y is 4 units upwards from (3, 0, 5)
z is 5 units inwards from (3, 4, 0)
Note that the x-axis has the equation ‘y=0, z=0’, because the axis is horizontal and always has a y and z values of 0 for all x.
Therefore, the distance of point P(3,4,5) from X-axis is the hypotenuse of the triangle formed by the upward and inward movement along y and z-axis, which can be found using Pythagoras’ Theorem:
sqrt(52 + 42 ) = sqrt(41)
The distance is the square root of 41.

Test: Introduction To Three Dimensional Geometry- 1 - Question 2

The direction cosines of X -axis are

Detailed Solution for Test: Introduction To Three Dimensional Geometry- 1 - Question 2

The x-axis makes angles 0°, 90° and 90° with x, y and z-axis. Again y-axis makes angles 0°, 90°, 90° with x, y and z-axis. 
∴ direction cosines of x-axes are cos 0°, cos 90°, cos 90° i.e. 1, 0, 0.

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test: Introduction To Three Dimensional Geometry- 1 - Question 3

The medians of a triangle are concurrent at the point called

Test: Introduction To Three Dimensional Geometry- 1 - Question 4

The direction cosines of any normal to the XY plane are

Detailed Solution for Test: Introduction To Three Dimensional Geometry- 1 - Question 4

Any normal of x−y plane is along z−axis.
normal unit vector to x−y plane, 
n→ = kˆ= 0iˆ+0jˆ+1kˆ
Direction cosines are <0, 0, 1> or
n→ = k =0iˆ+0jˆ−1kˆ
Direction cosines are <0, 0, −1>

Test: Introduction To Three Dimensional Geometry- 1 - Question 5

How many lines through the origin make equal angles with the coordinate axes?

Detailed Solution for Test: Introduction To Three Dimensional Geometry- 1 - Question 5

There are two different lines that make equal angles with the coordinate axes.
The are y = x line and y = - x line.
The y = x line divides the 1st and 3rd quadrant equally and makes a 45° angle with the positive direction of the x-axis and the y-axis and negative direction of the x-axis and the y-axis.
Again, the line y = - x divides the 2nd and 4th quadrant equally and makes a 45° angle with the positive direction of the x-axis and negative direction of the y-axis & negative direction of the x-axis and positive direction of the y-axis.

Test: Introduction To Three Dimensional Geometry- 1 - Question 6

The numbers 3, 4 , 5 can be

Detailed Solution for Test: Introduction To Three Dimensional Geometry- 1 - Question 6

Correct Answer : c

Explanation :  l2 + m2 + n2 = 1

(a) 9 + 16 + 25 not equal to 1

(b) y = 4z

4 is not equal to 20

(d) x + y - z = 0

3 + 4 - 5 = 0

=> 2 is not equal to 0

There option c satisfies the equation.

Test: Introduction To Three Dimensional Geometry- 1 - Question 7

If the direction cosines of a straight line are < k , k , k > , then

Detailed Solution for Test: Introduction To Three Dimensional Geometry- 1 - Question 7

Given that direction cosine of the line(k,k,k)
The value of k = +-1/(3)½
We know the sum of the squares of the direction cosine is one.
k2 + k2+ k2 = 1
3k2 = 1
k2 = +-1/(3)½

Test: Introduction To Three Dimensional Geometry- 1 - Question 8

Volume of a tetrahedron is k X area of one face X length of perpendicular from the opposite vertex upon it, where k is

Detailed Solution for Test: Introduction To Three Dimensional Geometry- 1 - Question 8

Correct Answer : C

Explanation :  Volume of tetrahedron = k(Area of one face) * (length of perpendicular from the opposite vertex upon it)

1/3 *(Area of one face) * (length of perpendicular from the opposite vertex upon it)

k = 1/3

Test: Introduction To Three Dimensional Geometry- 1 - Question 9

The radius of the sphere through the points (4 ,3 , 0) , (0 , 4 , 3) ,(0 , 5 , 0) and (4 , 0 , 3) is

Test: Introduction To Three Dimensional Geometry- 1 - Question 10

The points (4,7,8) ,(2, 3,4),(- 1, -2 , 1) and (1, 2, 5) are the vertices of a

Detailed Solution for Test: Introduction To Three Dimensional Geometry- 1 - Question 10

ABCD is a parallelogram for this we'll show that both the diagonal meet at 0 i.e., 0 is the midpoint of AC and BD
AC = [(4-1)/2, (7-2)/2, (8+1)/2]
      = [3/2, 5/2, 9/2]
BD = [(2+1)/2, (3+2)/2, (4+5)/2]
      = [3/2, 5/2, 9/2]

Test: Introduction To Three Dimensional Geometry- 1 - Question 11

The equation xy = 0 in three dimensional space represents

Test: Introduction To Three Dimensional Geometry- 1 - Question 12

The graph of the equation x2+y2 = 0 in the three dimensional space is

Test: Introduction To Three Dimensional Geometry- 1 - Question 13

In three dimensional space, locus of the equation x2+z2 = 0x2+z2 = 0 is

Test: Introduction To Three Dimensional Geometry- 1 - Question 14

The distance of the point (x , y , z) from the XY –plane is

Test: Introduction To Three Dimensional Geometry- 1 - Question 15

The angle between the lines x = 1 , y = 2 and y = - 1 , z = 0 is

Detailed Solution for Test: Introduction To Three Dimensional Geometry- 1 - Question 15

Given lines are
(x-1)/0 = (y-2)/0 = z/1
and x/1=(y+1)0=z/0
∴ cosθ=0⋅1+0⋅0+1⋅0=0
⇒ θ=90

Test: Introduction To Three Dimensional Geometry- 1 - Question 16

The line x = 1 , y = 2 is

Test: Introduction To Three Dimensional Geometry- 1 - Question 17

The equation (x – 1) (x – 2) = 0 represents, in three dimensional space, a

Test: Introduction To Three Dimensional Geometry- 1 - Question 18

A point (x , y , z) moves parallel to X- axis. Which of the three variables x , y , z remain fixed ?

Test: Introduction To Three Dimensional Geometry- 1 - Question 19

A point (x , y , z) moves parallel to XY - plane. Which of the three variables x, y, z remain fixed ?

Test: Introduction To Three Dimensional Geometry- 1 - Question 20

The plane x=0 divides the joinning of (−2,3,4) and (1,−2,3) in the ratio :

Detailed Solution for Test: Introduction To Three Dimensional Geometry- 1 - Question 20

Given place : x=0 and two points →(−2,3,4) and (1,−2,3)

let say a point (x,y,z) in x=0 place

So, x=(m+n(−2))/m+n

0=(m−2n)/m+n

0 = (m−2n)/m+n  ⇒m=2n

So, m/n = 2/1

⇒ 2:1 

Test: Introduction To Three Dimensional Geometry- 1 - Question 21

The direction cosines of the line joining (1 , - 1 , 1) , and (-1 , 1 , 1) are

Test: Introduction To Three Dimensional Geometry- 1 - Question 22

The line 

Test: Introduction To Three Dimensional Geometry- 1 - Question 23

The line x = x1, y = y1 is

Test: Introduction To Three Dimensional Geometry- 1 - Question 24

The locus of the equation xy + yz = 0 is

Test: Introduction To Three Dimensional Geometry- 1 - Question 25

The number of spheres of a given radius r and touching the coordinate axes is

75 videos|238 docs|91 tests
Information about Test: Introduction To Three Dimensional Geometry- 1 Page
In this test you can find the Exam questions for Test: Introduction To Three Dimensional Geometry- 1 solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Introduction To Three Dimensional Geometry- 1, EduRev gives you an ample number of Online tests for practice

Top Courses for Commerce

75 videos|238 docs|91 tests
Download as PDF

Top Courses for Commerce