are cosines of Direction angles

arecotangents of Direction angles

are tangents of Direction angles

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JEE Exam > JEE Tests > Test: Vector Algebra- 1 - JEE MCQ

Test: Vector Algebra- 1 - JEE MCQ

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25 Questions MCQ Test - Test: Vector Algebra- 1

Test: Vector Algebra- 1 for JEE 2024 is part of JEE preparation. The Test: Vector Algebra- 1 questions and answers have been prepared according to the JEE exam syllabus.The Test: Vector Algebra- 1 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Vector Algebra- 1 below.

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Test: Vector Algebra- 1 - Question 1

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Vector has

A.
direction
B.
magnitude
C.
magnitude as well as direction
D.
None of these

Detailed Solution for Test: Vector Algebra- 1 - Question 1

A vector has both magnitude as well as direction.

Test: Vector Algebra- 1 - Question 2

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Correct form of distributive law is

Detailed Solution for Test: Vector Algebra- 1 - Question 2

Distributive law is given by :

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Test: Vector Algebra- 1 - Question 3

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Magnitude of the vector

A.
1
B.
1.5
C.
0.5
D.
√3

Detailed Solution for Test: Vector Algebra- 1 - Question 3

We have :

Test: Vector Algebra- 1 - Question 4

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Find the unit vector in the direction of vector where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively

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Test: Vector Algebra- 1 - Question 5

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If is a non zero vector of magnitude ‘a’ and λ a non zero scalar, then λ is a unit vector if

A.
a = |λ|
B.
λ = 1
C.
λ = −1
D.

Detailed Solution for Test: Vector Algebra- 1 - Question 5

Test: Vector Algebra- 1 - Question 6

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Find the values of x and y so that the vectors are equal

A.
x = 2, y = 3
B.
x = 3, y = 3
C.
x = 3, y = 2
D.
x = 2, y = 2

Detailed Solution for Test: Vector Algebra- 1 - Question 6

Test: Vector Algebra- 1 - Question 7

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If P₁(x₁, y₁, z₁) and P₂(x₂, y₂, z₂) are any two points, then the vector joining P1 and P2is the vector P1P2. Magnitude of the vector

Detailed Solution for Test: Vector Algebra- 1 - Question 7

If P₁(x₁, y₁, z₁) and P₂(x₂, y₂, z₂) are any two points, then the vector joining P1 and P2is the vector P1P2, then ;

Test: Vector Algebra- 1 - Question 8

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Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7).

Detailed Solution for Test: Vector Algebra- 1 - Question 8

The scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7) is given by : (- 5 – 2) i.e. – 7 and (7 – 1) i.e. 6. Therefore, the scalar components are – 7 and 6 .,and vector components are

Test: Vector Algebra- 1 - Question 9

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Find a vector in the direction of the vector which has a magnitude of 8 units

Detailed Solution for Test: Vector Algebra- 1 - Question 9

Test: Vector Algebra- 1 - Question 10

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Find , if and

A.
17√2
B.
19√3
C.
8√3
D.
19√5

Detailed Solution for Test: Vector Algebra- 1 - Question 10

Test: Vector Algebra- 1 - Question 11

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Direction angles are angles

A.
that show the tip of the vector
B.
The angles α,β,γ made by the position vector with the positive directions of x, y and z-axes respectively
C.
The angles α,β,γ made by the perpendicular to position vector with the positive directions of x, y and z-axes respectively
D.
None of these

Detailed Solution for Test: Vector Algebra- 1 - Question 11

α,β,γ are the angles which the position vector makes with the positive x-axis ,y-axis and z-axis respectively are called direction angles.

Test: Vector Algebra- 1 - Question 12

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are any three vectors then the correct expression for distributivity of scalar product over addition is

Detailed Solution for Test: Vector Algebra- 1 - Question 12

are any three vectors then the correct expression for distributivity of scalar product over addition is :

Test: Vector Algebra- 1 - Question 13

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Find the values of x and y so that the vectors

A.
x = 2, y = 3
B.
x = 3, y = 3
C.
x = 2, y = 2
D.
x = 3, y = 2

Detailed Solution for Test: Vector Algebra- 1 - Question 13

Test: Vector Algebra- 1 - Question 14

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Find the direction cosines of the vector

Detailed Solution for Test: Vector Algebra- 1 - Question 14

Test: Vector Algebra- 1 - Question 15

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A.
45
B.
20
C.
48.5
D.
25√2

Detailed Solution for Test: Vector Algebra- 1 - Question 15

Test: Vector Algebra- 1 - Question 16

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Direction cosines

A.
are cosines of Direction angles
B.
arecotangents of Direction angles
C.
are tangents of Direction angles
D.
aresines of Direction angles

Detailed Solution for Test: Vector Algebra- 1 - Question 16

Cosines of the angles α,β,γ are called direction cosines.

Test: Vector Algebra- 1 - Question 17

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Magnitude of the vector

A.
√2
B.
√3
C.
1-√3
D.
1+√3

Detailed Solution for Test: Vector Algebra- 1 - Question 17

We have :

Test: Vector Algebra- 1 - Question 18

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Find the sum of the vectors and

Detailed Solution for Test: Vector Algebra- 1 - Question 18

We have:

Test: Vector Algebra- 1 - Question 19

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Find the direction cosines of the vector joining the points A(1, 2, –3) and B(–1, –2, 1), directed from A to B.

Detailed Solution for Test: Vector Algebra- 1 - Question 19

Therefore, the D.C.’s of vector AB are given by:

Test: Vector Algebra- 1 - Question 20

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If a unit vector makes angles π/3 with and an acute angle θ with then find θ

Detailed Solution for Test: Vector Algebra- 1 - Question 20

Test: Vector Algebra- 1 - Question 21

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If l, m and n are direction cosines of the position vector OP the coordinates of P are

A.
lr, mr and nr
B.
lr, m and nr
C.
l, mr and nr
D.
lr, mr and n

Detailed Solution for Test: Vector Algebra- 1 - Question 21

If l , m and n are the direction cosines of vector then , the coordinates of point P are given by : lr ,mr and nr respectively.

Test: Vector Algebra- 1 - Question 22

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Unit vectors along the axes OX, OY and OZ are denoted by

Detailed Solution for Test: Vector Algebra- 1 - Question 22

represents the unit vectors along the co ordinate axis i.e. OX ,OY and OZ respectively.

Test: Vector Algebra- 1 - Question 23

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Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

Detailed Solution for Test: Vector Algebra- 1 - Question 23

Test: Vector Algebra- 1 - Question 24

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Find the angle between two vectors with magnitudes and 2, respectively, having

Detailed Solution for Test: Vector Algebra- 1 - Question 24

Test: Vector Algebra- 1 - Question 25

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If a unit vector makes angles and an acute angle θ with , then the components of are

Detailed Solution for Test: Vector Algebra- 1 - Question 25

Let It is given that left| , then ,

Putting these values in (1) , we get :

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