Test: Introduction To Vector Algebra


20 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Introduction To Vector Algebra


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This mock test of Test: Introduction To Vector Algebra for JEE helps you for every JEE entrance exam. This contains 20 Multiple Choice Questions for JEE Test: Introduction To Vector Algebra (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Introduction To Vector Algebra quiz give you a good mix of easy questions and tough questions. JEE students definitely take this Test: Introduction To Vector Algebra exercise for a better result in the exam. You can find other Test: Introduction To Vector Algebra extra questions, long questions & short questions for JEE on EduRev as well by searching above.
QUESTION: 1

If a, b, c and d are the position vectors of the points A, B, C and D such that a + c = b + d, then ABCD is a​

Solution:
QUESTION: 2

For what values of x and y, the vectorsare equal?

Solution:

For equal vector
2x=3
and 2x=y

QUESTION: 3

Two or more vectors having the same initial point are called​

Solution: Two or more vectors having the same initial point are called coinitial vector. Two or more vectors are said to be collinear,if they are parallel to the same line,irrespective of their magnitudes and directions.
QUESTION: 4

If  ,the vectors a and b are ______ .​

Solution:

QUESTION: 5

If the magnitude of the position vector is 7, the value of x is:​

Solution:


7 = (x2 + 22 + (2x)2)1/2
49 = x2 + 22 + 4x2
= 4 + 5x2
5x2 = 45
x2 = 9
x = ±3

QUESTION: 6

If  , then

Solution:

QUESTION: 7

What is the additive identity of a vector?​

Solution:
QUESTION: 8

The angles α, β, γ made by the vector with the positive directions of X, Y and Z-axes respectively, then the direction cosines of the vector are: 

Solution:

cos α, cos β, cos γ
As per the definition of Direction Cosines.

QUESTION: 9

If a and b are the position vectors of two points A and B and C is a point on AB produced such that AC = 3AB, then position vector of C will be​

Solution:

AC = 3AB

(c - a)= 3(b - a). (c - a)

          = 3b -3a

c= 3b--2a

QUESTION: 10

Vector of magnitude 1 is called.​

Solution: A vector whose magnitude (i.e., length) is equal to 1 is called a unit vector. There are exactly two unit vectors in any given direction and one is the negative of the other.
QUESTION: 11

If  and , then the value of scalars x and y are:

Solution:

a = i + 2j

b = -2i + j

c = 4i +3j

c = xa +yb

4i + 3j  = x*(i + 2j) + y*(-2i +j)

= xi + 2xj - 2yi + yj

= (x-2y)i + (2x+y)j

So,

x-2y = 4

2x+y = 3

After solving,            

x = 2

y = -1

QUESTION: 12

The direction of zero vector.​

Solution:

Zero vector is the unit vector having zero length ,hence the direction is undefined.

QUESTION: 13

The unit vector in the direction of , where A and B are the points (2, – 3, 7) and (1, 3, – 4) is:

Solution:

Point A(2,-3,7)

Point B(1,3,-4)

Let vector in the direction of AB be C.

So,

C=B- A

 = (1,3,-4) - (2,-3,7)

 = (1-2 , 3+3 , -4-7 )

 = (-1,6,-11)

 = -1i + 6j -11k

 

Unit_vector = (Vector)/(Magnitude of vector)


C = (C_vector)/(Magnitude of C_vector)  = (-1i + 6j -11k)/158

QUESTION: 14

If a be magnitude of vector  then​

Solution:

Since a is the magnitude of the vector, it is always positive and it can be 0 in case of zero vectors.        
So, a ≥ 0

QUESTION: 15

A vector of magnitude 14 units, which is parallel to the vector

Solution:

Magnitude of i+2j-3k
=√[1^2+2^2+(-3)^2]=√14
= 14(i+2j-3k)/√14

QUESTION: 16

For any two vectors a and b​

Solution:
QUESTION: 17

Vectors that may be subject to its parallel displacement without changing its magnitude and direction are called _________.​

Solution:

A vector whose point of application is not fixed but magnitude and direction is, is called free vector. They are vectors which you can move anywhere in the plane. Free vectors are those who do not have a specified position in the plane. Also it can be moved parallel to itself.

QUESTION: 18

A vector whose initial and terminal points coincide, is called​

Solution:

A vector whose initial and terminal points coincide has no particular direction and 0 magnitude. Therefore, it is called zero vector.

QUESTION: 19

A point from a vector starts is called …… and where it ends is called its ……​

Solution:

A vector is a specific quantity drawn as a line segment with an arrowhead at one end. It has an initial point, where it begins, and a terminal point, where it ends. A vector is defined by its magnitude, or the length of the line, and its direction, indicated by an arrowhead at the terminal point.

QUESTION: 20

If  are position vectors of the points (- 1, 1) and (m, – 2). then for what value of m, the vectors  are collinear. 

Solution:

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