Three Dimensional Geometry - 1 - JEE MCQ

# Three Dimensional Geometry - 1 - JEE MCQ

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## 30 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Three Dimensional Geometry - 1

Three Dimensional Geometry - 1 for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Three Dimensional Geometry - 1 questions and answers have been prepared according to the JEE exam syllabus.The Three Dimensional Geometry - 1 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Three Dimensional Geometry - 1 below.
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Three Dimensional Geometry - 1 - Question 1

### Skew lines are lines in different planes which are

Detailed Solution for Three Dimensional Geometry - 1 - Question 1

By definition : The Skew lines are lines in different planes which are neither parallel nor intersecting .

Three Dimensional Geometry - 1 - Question 2

### In the following case, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. 2x – y + 3z – 1 = 0 and 2x – y + 3z + 3 = 0

Detailed Solution for Three Dimensional Geometry - 1 - Question 2

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Three Dimensional Geometry - 1 - Question 3

### The equation of a plane through a point whose position vector is  perpendicular to the vector  . is

Detailed Solution for Three Dimensional Geometry - 1 - Question 3

In vector form The equation of a plane through a point whose position vector is  perpendicular to the vector  Is given by :

Three Dimensional Geometry - 1 - Question 4

If l1, m1, n1 and l2, m2, n2 are the direction cosines of two lines; and θ is the acute angle between the two lines; then

Detailed Solution for Three Dimensional Geometry - 1 - Question 4

If l1, m1, n1 and l2, m2, n2 are the direction cosines of two lines; and θ is the acute angle between the two lines; then the cosine of the angle between these two lines is given by :

Three Dimensional Geometry - 1 - Question 5

Find the distance of the point (0, 0, 0) from the plane 3x – 4y + 12 z = 3

Detailed Solution for Three Dimensional Geometry - 1 - Question 5

As we know that the length of the perpendicular from point
P(x1,y1,z1) from the plane a1x+b1y+c1z+d1 = 0 is given by:

Three Dimensional Geometry - 1 - Question 6

If a1, b1, c1 and a2, b2, c2 are the direction ratios of two lines and θ is the acute angle between the two lines; then

Detailed Solution for Three Dimensional Geometry - 1 - Question 6

If a1, b1, c1 and a2, b2, c2 are the direction ratios of two lines and θθ is the acute angle between the two lines; then , the cosine of the angle between these two lines is given by :

Three Dimensional Geometry - 1 - Question 7

The vector and cartesian equations of the planes that passes through the point (1, 0, – 2) and the normal to the plane is

Detailed Solution for Three Dimensional Geometry - 1 - Question 7

Let
be the position vector of the point  here,
. Therefore, the required vector equation of the plane is:

Three Dimensional Geometry - 1 - Question 8

Detailed Solution for Three Dimensional Geometry - 1 - Question 8

Three Dimensional Geometry - 1 - Question 9

If the coordinates of point A, B, C are (–1, 3, 2), (2, 3, 5) and (3, 5, –2) respectively then angle A is

Detailed Solution for Three Dimensional Geometry - 1 - Question 9

Three Dimensional Geometry - 1 - Question 10

The projection of a line on the axes are 2, 3, 6 then the length of line is

Detailed Solution for Three Dimensional Geometry - 1 - Question 10

Three Dimensional Geometry - 1 - Question 11

Detailed Solution for Three Dimensional Geometry - 1 - Question 11

Three Dimensional Geometry - 1 - Question 12

OABC is a tetrahedron whose vertices are O(0, 0, 0) ; A(a, 2, 3) ; B(1, b, 2) and C(2, 1, c). If its centroid be (1, 2, –1) then distance of the point (a, b, c) from the origin is

Detailed Solution for Three Dimensional Geometry - 1 - Question 12

Three Dimensional Geometry - 1 - Question 13

Find the direction cosines of line joining points (1, –1, –3) and (–1, 2, 3)

Detailed Solution for Three Dimensional Geometry - 1 - Question 13

Three Dimensional Geometry - 1 - Question 14

A mirror and a source of light are situated at the origin O and at a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the DRs of the normal to the plane of mirror are 1, –1, 1, then DCs for the reflected ray are -

Detailed Solution for Three Dimensional Geometry - 1 - Question 14

Three Dimensional Geometry - 1 - Question 15

Foot of perpendicular from (1, 2, 3) to the line joining points (6, 7, 7) and (9, 9, 5) is-

Detailed Solution for Three Dimensional Geometry - 1 - Question 15

Three Dimensional Geometry - 1 - Question 16

Detailed Solution for Three Dimensional Geometry - 1 - Question 16

Three Dimensional Geometry - 1 - Question 17

If x + y + z = 0, | x | = | y | = | z | = 2 and θ is angle between y and z. then the value of cosec2θ  + cot2θ is equal to

Detailed Solution for Three Dimensional Geometry - 1 - Question 17

Three Dimensional Geometry - 1 - Question 18

Detailed Solution for Three Dimensional Geometry - 1 - Question 18

Three Dimensional Geometry - 1 - Question 19

Detailed Solution for Three Dimensional Geometry - 1 - Question 19

Three Dimensional Geometry - 1 - Question 20

A line passing through A(1, 2, 3) and having direction ratios (3, 4, 5) meets a plane x + 2y – 3z = 5 at B, then distance AB is equal to-

Detailed Solution for Three Dimensional Geometry - 1 - Question 20

Three Dimensional Geometry - 1 - Question 21

The shortest distance between a diagonal of a cube of edge-length one unit and the edge not meeting it, is -

Detailed Solution for Three Dimensional Geometry - 1 - Question 21

dr’s of diagonal through the origin are (1, 1, 1)

Three Dimensional Geometry - 1 - Question 22

Angle between the rays with d.r.'s 4, – 3, 5 & 3, 4, 5 is-

Detailed Solution for Three Dimensional Geometry - 1 - Question 22

Three Dimensional Geometry - 1 - Question 23

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

Detailed Solution for Three Dimensional Geometry - 1 - Question 23

Three Dimensional Geometry - 1 - Question 24

The equation xy = 0 in three dimensional space represents -

Detailed Solution for Three Dimensional Geometry - 1 - Question 24

xy = 0 ⇔ x = 0 or y = 0. Hence locus of xy = 0 is the union of all points which lie in YOZplane or on ZOX-plane. So the equation xy = 0 represents a pair of perpendicular planes.

Three Dimensional Geometry - 1 - Question 25

The volume of the tetrahedron included between the plane 3x + 4y –5z – 60 = 0 and the coordinate planes in cubic units is

Detailed Solution for Three Dimensional Geometry - 1 - Question 25

Three Dimensional Geometry - 1 - Question 26

If the sum of the squares of the distance of a point from the three co-ordinate axes be 36, then its distance from the origin is

Detailed Solution for Three Dimensional Geometry - 1 - Question 26

Three Dimensional Geometry - 1 - Question 27

Detailed Solution for Three Dimensional Geometry - 1 - Question 27

Three Dimensional Geometry - 1 - Question 28

Detailed Solution for Three Dimensional Geometry - 1 - Question 28

Three Dimensional Geometry - 1 - Question 29

If the sum of the squares of the distance of a point from the three co-ordinate axes be 36, then its distance from the origin is

Detailed Solution for Three Dimensional Geometry - 1 - Question 29

Three Dimensional Geometry - 1 - Question 30

If the foot of perpendicular drawn from the origin to the plane is (4, – 2, – 5). Then equation of plane is

Detailed Solution for Three Dimensional Geometry - 1 - Question 30

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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests