Scalar and Vector Product MCQ Quiz - Objective Question with Answer for Scalar and Vector Product - Download Free PDF

Last updated on Jul 8, 2025

Latest Scalar and Vector Product MCQ Objective Questions

Scalar and Vector Product Question 1:

The position vectors of three points A, B and C respectively, where   and   respectively, where . What is  equal to?

  1. Unit vector

Answer (Detailed Solution Below)

Option 1 :

Scalar and Vector Product Question 1 Detailed Solution

Calculation:

Given,

The position vectors of points A, B, and C are , , and respectively, and .

The expression to evaluate is: .

First, substitute into the equation:

.

Using the distributive property of the cross product:

.

Since and , we are left with:

.

Substitute into the expression:

.

Factor out

.

Since , the expression becomes:

.

∴ The final result is .

Hence, the correct answer is option 1. 

Scalar and Vector Product Question 2:

A line makes angles α, β and γ with the positive directions of the coordinate axes. If , then what is equal to?

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

Answer (Detailed Solution Below)

Option 4 : 2

Scalar and Vector Product Question 2 Detailed Solution

Calculation:

Given,

Using the identity , we substitute:

Simplifying the equation:

Rearrange to isolate the sine terms:

Now, calculate the dot product:

∴ The value of is 2.

Hence, the correct answer is Option 4.

Scalar and Vector Product Question 3:

Let and . Then is equal to

Answer (Detailed Solution Below)

Option 2 :

Scalar and Vector Product Question 3 Detailed Solution

Calculation: 

Taking the cross product with 

Hence, the correct answer is Option 2.

Scalar and Vector Product Question 4:

If two vectors  and  is given by  and  and the vectors  and  are related as  and . Then  is equal to

  1. 12
  2. 8
  3. 10
  4. 7

Answer (Detailed Solution Below)

Option 3 : 10

Scalar and Vector Product Question 4 Detailed Solution

Answer (3)

Sol.

dot with 

= 5 × 1 + (–2) (2) + (3) (3)

= 5 – 4 + 9 = 10

Scalar and Vector Product Question 5:

If  and  then, The unit vector in the direction of  is . The value of x is  

Answer (Detailed Solution Below) 4

Scalar and Vector Product Question 5 Detailed Solution

Calculation:

The vector is 

 

⇒  x = 4

Top Scalar and Vector Product MCQ Objective Questions

Answer (Detailed Solution Below)

Option 2 : 0

Scalar and Vector Product Question 6 Detailed Solution

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Concept:

Dot product of two vectors is defined as:

Cross/Vector product of two vectors is defined as:

where θ is the angle between 

Calculation:

To Find: Value of 

Here angle between them is 0°

The sine of the angle between vectors  and  is

Answer (Detailed Solution Below)

Option 2 :

Scalar and Vector Product Question 7 Detailed Solution

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Concept:

If  then

Calculation:

Given:  and

The value of λ if the vectors  and  are parallel is

Answer (Detailed Solution Below)

Option 1 :

Scalar and Vector Product Question 8 Detailed Solution

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The given two vectors are in parallel, therefore the vector product of these two vectors will be zero.

⇒ 9λ – 6 = 0 and 2 - 3λ = 0

∴ λ = 2/3

Answer (Detailed Solution Below)

Option 3 :

Scalar and Vector Product Question 9 Detailed Solution

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Given: 

Concept:

î × î  = ĵ × ĵ = k̂ × k̂  = 0 

î × ĵ = k̂ , ĵ × k̂ = î , k̂ × î = ĵ 

Calculation:

Let a = mî + nĵ +lk̂ 

According to the Question 

 = î  × (mî + nĵ +lk̂  × î) + ĵ ×  (mî + nĵ +lk̂  × ĵ) + k̂ × (mî + nĵ +lk̂  × k̂)

 =  î  × (-nk̂ + lĵ) + ĵ × (mk̂ -lî  ) + k̂ × (-mĵ + nî) 

 = nĵ  + lk̂ + mî +  lk̂ + mî + nĵ 

 = 2(mî + nĵ +lk̂ ) = 2

∴ The correct option is 3

What is the value of λ for which the vectors  are coplanar 

  1. 5
  2. 4
  3. 2
  4. 1

Answer (Detailed Solution Below)

Option 4 : 1

Scalar and Vector Product Question 10 Detailed Solution

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Concept:

Condition for coplanarity:

Calculation:

Here,  are coplanar

1(λ - 1) + 1(2λ + λ) + 1(-2 - λ) = 0

λ - 1 + 2λ + λ + -2 - λ = 0

3λ - 3 = 0

λ = 1

Hence, option (4) is correct.

If , then find the value of 

  1. √3
  2. 8√3 
  3. 6√3 
  4. 4√3 

Answer (Detailed Solution Below)

Option 3 : 6√3 

Scalar and Vector Product Question 11 Detailed Solution

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Concept:

Let  are two vectors

  is the unit vector perpendicular to both 

 

Calculation:

Given: 

As we know, 

⇒ 6 = 3 × 4 × cos θ 

⇒ cos θ = 

∴ θ = 60° 

As we know that, If  are two vectors, then

      (∵ Magnitude of a unit vector is one)

 = 3 × 4 × sin 60° 

If  is a unit vector and , then find .

  1. 4
  2. 7
  3. 8
  4. 2

Answer (Detailed Solution Below)

Option 1 : 4

Scalar and Vector Product Question 12 Detailed Solution

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Concept:

If  is a unit vector, then .

 

Calculation:

It is given that .

⇒ 

Since  is a unit vector, we get:

⇒ 

⇒ 

⇒  = 4

A unit vector perpendicular to each of the vectors 2î - ĵ + k̂ and 3î - 4ĵ - k̂ is

Answer (Detailed Solution Below)

Option 1 :

Scalar and Vector Product Question 13 Detailed Solution

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Concept:

  • Unit vector: a vector which has a magnitude of one.

 

Let

Magnitude of vector of a =

Unit vector =

  • Let  and  be the two vectors, then the vector  perpendicular to both  and

 

 and

 

  • If  then determinant of A is given by:

 

|A| = a11 × {(a22 × a33) - (a23 × a32)} - a12 × {(a21 × a33) - (a23 × a31)} + a13 × {(a21 × a32) - (a22 × a31)}

Calculation:

Let vector  and  and vector  perpendicular to both  and 

Unit vector =

Answer (Detailed Solution Below)

Option 3 :

Scalar and Vector Product Question 14 Detailed Solution

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Concept:  

Calculation:

Given

 

Additional Information

Properties of Scalar Product

 (Scalar product is commutative)

 (Distributive of scalar product over addition)

In terms of orthogonal coordinates for mutually perpendicular vectors, it is seen that 

Properties of Vector Product

 (non-commutative)

  (Distributive of vector product over addition)

If  are mutually perpendicular vectors of equal magnitude, then the angle between  and  is

  1. cos−1 (1/3)
  2. cos−1 (1/√3)
  3. 90°

Answer (Detailed Solution Below)

Option 2 : cos−1 (1/√3)

Scalar and Vector Product Question 15 Detailed Solution

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Concept:

Dot Product: it is also called the inner product or scalar product

  • Let the two vectors be  then dot Product of two vector:   Where, || = Magnitude of vectors a and || = Magnitude of vectors b and θ is angle between a and b 

 

Calculation:

Let

⇒ 1 + 0 + 0 = √3 × 1 × cos θ

⇒ cos θ = 1/√3

∴ θ = cos−1 (1/√3)

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