Magnitude and Directions of a Vector MCQ Quiz - Objective Question with Answer for Magnitude and Directions of a Vector - Download Free PDF

Last updated on May 1, 2025

Latest Magnitude and Directions of a Vector MCQ Objective Questions

Magnitude and Directions of a Vector Question 1:

Find the magnitude of vector , where ?

  1. 40

Answer (Detailed Solution Below)

Option 1 :

Magnitude and Directions of a Vector Question 1 Detailed Solution

Concept:

Magnitude of vector  then magnitude of vector is given by 

Calculation:

Given: Let where 

⇒ 

As we know that, if  then 

⇒ |

⇒  

Hence, option 1 is correct.

Magnitude and Directions of a Vector Question 2:

The magnitude of a given vector with end points (5, –5, 0) and (2, 3, 0) must be ______.

  1. None of the above

Answer (Detailed Solution Below)

Option 4 :

Magnitude and Directions of a Vector Question 2 Detailed Solution

Given:

The vector with end points (5, –5, 0) and (2, 3, 0) 

Concept:

Let  be the position vector of the points A and B respectively,

then the vector equation of the line passing through A and B is given by I  I = II

Calculation:

Let the position vector of points A (-1, 0, 2) and B (3, 4, 6) be  and  respectively.

Then, 

And, 

⇒  

⇒ I  I = II

⇒ I  I 

⇒ I  I ​√​73

∴ Correct answer is √​73.

Magnitude and Directions of a Vector Question 3:

The magnitude of a given vector with end points (5, –5, 0) and (2, 3, 0) must be ______.

Answer (Detailed Solution Below)

Option 4 :

Magnitude and Directions of a Vector Question 3 Detailed Solution

To determine the magnitude of a vector with given endpoints:

Calculation:

Step 1: Subtract the coordinates

Step 2: Square the differencesStep 3: Sum the squares

⇒ 9 + 64 + 0 = 73

Step 4: Take the square rootFinal Answer:

Hence, The Correct Answer is Option 4.

Magnitude and Directions of a Vector Question 4:

Given that , out of these three vectors two are equal in magnitude and the magnitude of the third vector times as that of either of the two having equal magnitude. Then the angles between vectors are given by :-

Answer (Detailed Solution Below)

Option 4 :

Magnitude and Directions of a Vector Question 4 Detailed Solution

Thus, angles are

Magnitude and Directions of a Vector Question 5:

Scalar projection of the line segment joining the points A(-2, 0,3), B(1, 4, 2) on the line whose direction ratios are 6, -2, 3 is

  1. 1
  2. 7

Answer (Detailed Solution Below)

Option 2 : 1

Magnitude and Directions of a Vector Question 5 Detailed Solution

Answer : 2

Solution :

Let a̅ be the vector joining A(-2, 0, 3) and B(1, 4, 2).

∴ 

and b = 

∴ Projection = 

 

= 1

Top Magnitude and Directions of a Vector MCQ Objective Questions

What is the value of p for which the vector p(2î - ĵ + 2k̂) is of 3 units length?

  1. 1
  2. 2
  3. 3
  4. 6

Answer (Detailed Solution Below)

Option 1 : 1

Magnitude and Directions of a Vector Question 6 Detailed Solution

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Concept:

Let  then magnitude of the vector of a = 

Calculation:

Let  =  p(2î - ĵ + 2k̂)

Given, 

⇒ 

⇒ 

⇒ 3p = 3

∴ p = 1

If A =  and B =  , then what is the value of ?

  1. 6√2
  2. 7√2
  3. 8√2
  4. 9√2

Answer (Detailed Solution Below)

Option 4 : 9√2

Magnitude and Directions of a Vector Question 7 Detailed Solution

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Concept:

If , then 

Calculation:

Given A =  and B = 

 = 

 = 

Now 

 = 9√2

If  = 2î + ĵ + k̂ and  = î + 2ĵ + k̂, then the magnitude of their resultant is:

  1. 2√5
  2. 2√6
  3. √22
  4. None of these.

Answer (Detailed Solution Below)

Option 3 : √22

Magnitude and Directions of a Vector Question 8 Detailed Solution

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Concept:

The magnitude of a vector  = a1î + a2ĵ + a3k̂ is given as .

The magnitude of the sum of vectors  and  can also be calculated as .

The resultant of a set of vectors acting at a point is simply the algebraic sum of the vectors.

Calculation:

The resultant of the vectors  = 2î + ĵ + k̂ and ​​ = î + 2ĵ + k̂ is:

 = (2î + ĵ + k̂) + (î + 2ĵ + k̂) = 3î + 3ĵ + 2k̂

Now, .

What is the value of k for which the vector k(2î -  ĵ -  2k̂) is of 6 units length?

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 2 : 2

Magnitude and Directions of a Vector Question 9 Detailed Solution

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Concept:

Length of the vector  from origin is 

Calculation:

Length of the vector k(2î -  ĵ -  2k̂) from origin is 

 

 

= 3k

Length is 6 units given

3k = 6

k = 6/3

k = 2

Hence option 2 is correct.

If  are two vectors then find the value of  ?

Answer (Detailed Solution Below)

Option 4 :

Magnitude and Directions of a Vector Question 10 Detailed Solution

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CONCEPT:

If  is a vector then magnitude of  is given by: 

CALCULATION:

Given: 

Here, we have to find the value of 

⇒ 

As we know that, if   then magnitude of  is given by: 

⇒ 

Hence, option D is the correct answer.

Find the direction cosines of the vector 7î + 4ĵ - 3k̂.

  1. Both options 1 and 2
  2. None of these

Answer (Detailed Solution Below)

Option 3 : Both options 1 and 2

Magnitude and Directions of a Vector Question 11 Detailed Solution

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Concept:

The direction cosines of the vector aî + bĵ + ck̂ are given by α = , β =  and γ = .

Calculation:

For the given vector 7î + 4ĵ - 3k̂, a = 7, b = 4 and c = -3.

The direction cosines of the vector are:

α = , β =  and γ = 

⇒ α = , β =  and γ =  

∴ (α , β , γ ) = () or (​)

The vector  is

  1. Parallel to
  2. Null vector
  3. Unit vector
  4. None of the above

Answer (Detailed Solution Below)

Option 3 : Unit vector

Magnitude and Directions of a Vector Question 12 Detailed Solution

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Concept:

Unit vector: a vector that has a magnitude of one.

  • Let
  • Magnitude of vector of a =
  • Unit vector =

 

Calculation:

Given Vector is

Now calculate the magnitude of Vector A,

So,  is a unit vector.

What are the values of x for which the angle between the vectors 2x2 + 3x +  and  −2 + x2 is obtuse ?

  1. 0 < x < 2
  2. x < 0
  3. x > 2
  4. 0 ≤ x ≤ 2

Answer (Detailed Solution Below)

Option 1 : 0 < x < 2

Magnitude and Directions of a Vector Question 13 Detailed Solution

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Concept:

  • The angle between two vectors   and  is given by, ​ 
  • If  = a1 + a2 + a3 and   = b1 + b2 + b3, then  

Calculation:

Given: The angle between the vectors 2x2 + 3x +  and  −2 + x2 is obtuse

The angle between the vectors 2x2 + 3x +  and  −2 + x2 is given by

⇒ 

⇒ 

Since θ is obtuse, 

⇒ cos θ

⇒ 3x2 - 6x

⇒ x(x - 2)

⇒ 0

∴ The correct option is (1).

If the position vectors of points A and B are  and  respectively, then what is the length of ?

  1. √5
  2. 3√5
  3. 2√5 
  4. 4

Answer (Detailed Solution Below)

Option 3 : 2√5 

Magnitude and Directions of a Vector Question 14 Detailed Solution

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Concept:

If A and B are points with position vectors  respectively then 

If  is a vector then the magnitude of the vector is given by

 

Calculation:

Given: The position vectors of points A and B are  and  respectively

As we know, If A and B are points with position vectors  respectively then 

As we know that, If  is a vector then the magnitude of the vector is given by

Answer (Detailed Solution Below)

Option 1 :

Magnitude and Directions of a Vector Question 15 Detailed Solution

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Given:

Calculation:

We have,

⇒ 

⇒          [∵ ]

⇒ 

⇒        []

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

Put the value of 

⇒ 

⇒  

∴   and 

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