JEE Exam  >  JEE Tests  >  Mathematics (Maths) for JEE Main & Advanced  >  Test: Introduction To 3D Geometry - JEE MCQ

Test: Introduction To 3D Geometry - JEE MCQ


Test Description

20 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Introduction To 3D Geometry

Test: Introduction To 3D Geometry for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Introduction To 3D Geometry questions and answers have been prepared according to the JEE exam syllabus.The Test: Introduction To 3D Geometry MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Introduction To 3D Geometry below.
Solutions of Test: Introduction To 3D Geometry questions in English are available as part of our Mathematics (Maths) for JEE Main & Advanced for JEE & Test: Introduction To 3D Geometry solutions in Hindi for Mathematics (Maths) for JEE Main & Advanced course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Introduction To 3D Geometry | 20 questions in 20 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) for JEE Main & Advanced for JEE Exam | Download free PDF with solutions
Test: Introduction To 3D Geometry - Question 1

Find the direction cosines of a line which makes equal angles with all three the coordinate axes.​

Detailed Solution for Test: Introduction To 3D Geometry - Question 1

Test: Introduction To 3D Geometry - Question 2

Three planes, viz the XY Plane, XZ Plane and the YZ Plane divide the space into eight parts. Each part is called an OCTANT. What is the relation between these three planes​

Detailed Solution for Test: Introduction To 3D Geometry - Question 2

The three mutually perpendicular coordinate planes which in turn divide the space into eight parts and each part is known as octant.

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

The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:​

Detailed Solution for Test: Introduction To 3D Geometry - Question 3


Test: Introduction To 3D Geometry - Question 4

If the direction cosines of a line from the positive X-axis and Y-axis areThe angle of the line through Z-axis is:​

Detailed Solution for Test: Introduction To 3D Geometry - Question 4



Test: Introduction To 3D Geometry - Question 5

The direction cosines of the line equally inclined with the axes are:​

Detailed Solution for Test: Introduction To 3D Geometry - Question 5

Test: Introduction To 3D Geometry - Question 6

The direction cosines of the line whose direction ratios are 6, – 6, 3 are:

Detailed Solution for Test: Introduction To 3D Geometry - Question 6

Test: Introduction To 3D Geometry - Question 7

Find the direction cosines of the x axis.​

Detailed Solution for Test: Introduction To 3D Geometry - Question 7

To find Direction Cosines of X-axis.
Take any two points on X-axis : A(a,0,0) & B(b,0,0)
DR of AB : (b-a,0,0)
DC of AB : ((b-a)/(((b-a)2 + 0 + 0)1/2), 0, 0)
: ((b-a)/(b-a) , 0 , 0)
: (1,0,0)

Test: Introduction To 3D Geometry - Question 8

The direction cosines of the line joining the points (2, -1, 8) and (-4, -3, 5) are:

Detailed Solution for Test: Introduction To 3D Geometry - Question 8

Pt. A(2, -1, 8)
Pt. B(-4, -3, 5)
Direction Ratio DR of AB : ( -4-2 , -3+1 , 5-8 )
: (-6,-2,-3)
Direction cosine of AB : ( -6/(62+22+32)1/2 , -2/(62+22+32)1/2 , -3/(62+22+32)1/2)
: ( -6/7, -2/7, -3/7)
 

Test: Introduction To 3D Geometry - Question 9

What are direction numbers of a line.​

Detailed Solution for Test: Introduction To 3D Geometry - Question 9

The numbers which are proportional to direction cosines of a line are called direction numbers of the line.

Test: Introduction To 3D Geometry - Question 10

What are direction ratios of a line.​

Test: Introduction To 3D Geometry - Question 11

Find the direction cosines of the side AB of the triangle whose vertices are A(3, 5, -4), B(-1, 1, 2) and C(-5, -5, -2)

Detailed Solution for Test: Introduction To 3D Geometry - Question 11

Test: Introduction To 3D Geometry - Question 12

If l, m , n are the direction cosines of any line, then sum of the squares of the direction cosines of the line is always​

Test: Introduction To 3D Geometry - Question 13

If a line has the direction ratios -4, 18, -12 then what are its direction cosines?​

Detailed Solution for Test: Introduction To 3D Geometry - Question 13

DR of the line :  (-4, 18 -12)
DC of the line : (-4/k, 18/k, -12/k)
where k = ((42) + (182) + (12)2)1/2
= (16 + 324 + 144)1/2
= (484)1/2
= 22
So, DC : (-4/22, 18/22, -12/22)
: (-2/11 , 9/11 , -6/11)

Test: Introduction To 3D Geometry - Question 14

The direction cosines of the line equally inclined with the axes, are:​

Detailed Solution for Test: Introduction To 3D Geometry - Question 14
Cos^2 alpha+cos ^2 beta +cos^ 2 gamma =1
put alpha =beta. =gamma
we get cosalpha= 1/√3
DC's of given line (1/√3,1/√3,1/3)
Test: Introduction To 3D Geometry - Question 15

If a line makes angles 45°,150°, 135°, with x, y and z-axes respectively, find its direction cosines.

Detailed Solution for Test: Introduction To 3D Geometry - Question 15

Test: Introduction To 3D Geometry - Question 16

Find the equation of the set of points which are equidistant from the points (1, 2 , 3) and (3, 2, -1)​

Detailed Solution for Test: Introduction To 3D Geometry - Question 16

Pt. A(1, 2 , 3)
Pt. B(3, 2, -1)
Let P(x,y,z)
So, AP = BP
((x-1)2 + (y-2)2 + (z-3)2)1/2 = ((x-3)2 + (y-2)2 + (z+1)2)1/2
(x-1)2 + (y-2)2 + (z-3)2) = (x-3)2 + (y-2)2 + (z+1)2
x2 +1 -2x + y2 + 4 - 4y + z2 + 9 – 6z = x2 +9 -6x + y2 + 4 - 4y + z2 + 1 + 2z
4x – 8z = 0
x – 2z = 0

Test: Introduction To 3D Geometry - Question 17

If a line in the ZX-plane makes an angle 60o with Z-axis, the direction cosines of this line are:

Detailed Solution for Test: Introduction To 3D Geometry - Question 17

Test: Introduction To 3D Geometry - Question 18

A line makes angles α, β, γ with the positive directions of X-axis, Y-axis and Z-axis, respectively, then the directions cosines of the line are:

Detailed Solution for Test: Introduction To 3D Geometry - Question 18

cos α, cos β, cos γ
By the definition of Direction Cosines

Test: Introduction To 3D Geometry - Question 19

The signs of the X,Y and Z coordinates of a point that lies in the octant OXYZ’ is​

Detailed Solution for Test: Introduction To 3D Geometry - Question 19

X,Y,Z imply positive X,Y,Z axis & X’,Y’,Z’ imply negative X,Y,Z axis.
So, OXYZ’ will have a point of signs (+, +, -).

Test: Introduction To 3D Geometry - Question 20

If a line in the ZX-plane makes an angle 30o with Z-axis, the direction cosines of this line are:

Detailed Solution for Test: Introduction To 3D Geometry - Question 20
The line makes 30o with z-axis

Since it is in z-x axis the angle made with y-axis is 90

And angle made by x-axis is 60

Therefore direction cosines are

1/2, 0, √3/2
209 videos|443 docs|143 tests
Information about Test: Introduction To 3D Geometry Page
In this test you can find the Exam questions for Test: Introduction To 3D Geometry solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Introduction To 3D Geometry, EduRev gives you an ample number of Online tests for practice

Top Courses for JEE

Download as PDF

Top Courses for JEE