Test: Vector Algebra- 2 - JEE MCQ

# Test: Vector Algebra- 2 - JEE MCQ

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## 25 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Vector Algebra- 2

Test: Vector Algebra- 2 for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Vector Algebra- 2 questions and answers have been prepared according to the JEE exam syllabus.The Test: Vector Algebra- 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Vector Algebra- 2 below.
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Test: Vector Algebra- 2 - Question 1

### Zero Vector

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

A vector whose initial and terminal points coincides is called Zero Vector. The magnitude of Zero Vector is also Zero.

Test: Vector Algebra- 2 - Question 2

### If a vector is expressed in component form as  then the magnitude of the vector  is

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Test: Vector Algebra- 2 - Question 3

### Find the value of x for which x  is a unit vector

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Test: Vector Algebra- 2 - Question 4

Find the angle between two vectors

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Test: Vector Algebra- 2 - Question 5

Find λ and μ if

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It is given that:

Test: Vector Algebra- 2 - Question 6

Unit Vector is

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The vector whose magnitude is always 1 or unity is called a Unit Vector.

Test: Vector Algebra- 2 - Question 7

If a vector  is expressed in component form as  then x, y and z are referred to as

Detailed Solution for Test: Vector Algebra- 2 - Question 7

In  x , y and z represents the components of along x-axis ,y-axis and z-axis respectively.

Test: Vector Algebra- 2 - Question 8

Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

Detailed Solution for Test: Vector Algebra- 2 - Question 8

Therefore , AB and BC are parallel, but point B is common , so points , A,B,C are collinear. As

Test: Vector Algebra- 2 - Question 9

Find the projection of the vector

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Test: Vector Algebra- 2 - Question 10

Let the vectors  be such that  is a unit vector if the angle between vectors  is

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Test: Vector Algebra- 2 - Question 11

The unit vector in the direction of a given vector

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is called the unit vector of a given vector

Test: Vector Algebra- 2 - Question 12

Which of the following is a vector?

Detailed Solution for Test: Vector Algebra- 2 - Question 12

Acceleration is a vector quantity , because acceleration is defined as the rate of change of velocity w.r.t. time.

Test: Vector Algebra- 2 - Question 13

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are  externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.

Detailed Solution for Test: Vector Algebra- 2 - Question 13

Let position vector of point R be . As point R divides externally the line segment PQ in the ratio 1:2 .therefore ,

Also , mid point of the line segment RQ is :
Which is the position vector of point P.
Therefore , P is the mid point of line segment RQ.

Test: Vector Algebra- 2 - Question 14

Find the projection of the vector  on the vector

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then projection of vector a on vector b is given by :

Test: Vector Algebra- 2 - Question 15

If θ is the angle between two vectors

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Test: Vector Algebra- 2 - Question 16

Coinitial Vectors are

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Two vectors whose initial point is same are called co- initial vectors

Test: Vector Algebra- 2 - Question 17

In the figure which are the Equal vectors?

Detailed Solution for Test: Vector Algebra- 2 - Question 17

are equal vectors , because they have equal magnitude and same direction.

Test: Vector Algebra- 2 - Question 18

The scalar product of two nonzero vectors

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The scalar product of two nonzero vectors by

Test: Vector Algebra- 2 - Question 19

Find if for a unit vector

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Test: Vector Algebra- 2 - Question 20

If θ is the angle between any two vectors  when θ is equal to

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Test: Vector Algebra- 2 - Question 21

Vectors A and BareCollinear

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Two vectors A and B are said to be collinear , if they are parallel to the same line irrespective of their magnitudes and directions.

Test: Vector Algebra- 2 - Question 22

Detailed Solution for Test: Vector Algebra- 2 - Question 22

collinear vectors , because they are parallel in direction and having the same magnitude.

Test: Vector Algebra- 2 - Question 23

The scalar product of two nonzero vectors

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The scalar product of two nonzero vectors

Test: Vector Algebra- 2 - Question 24

If   are unit vectors such that then, the value of

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It is given that :  are unit vectors such that
then :

Test: Vector Algebra- 2 - Question 25

Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5).

Detailed Solution for Test: Vector Algebra- 2 - Question 25

Therefore , the area of triangle

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## Mathematics (Maths) for JEE Main & Advanced

194 videos|554 docs|187 tests