Types of Vectors MCQ Quiz in मल्याळम - Objective Question with Answer for Types of Vectors - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Last updated on Apr 13, 2025

നേടുക Types of Vectors ഉത്തരങ്ങളും വിശദമായ പരിഹാരങ്ങളുമുള്ള മൾട്ടിപ്പിൾ ചോയ്സ് ചോദ്യങ്ങൾ (MCQ ക്വിസ്). ഇവ സൗജന്യമായി ഡൗൺലോഡ് ചെയ്യുക Types of Vectors MCQ ക്വിസ് പിഡിഎഫ്, ബാങ്കിംഗ്, എസ്എസ്‌സി, റെയിൽവേ, യുപിഎസ്‌സി, സ്റ്റേറ്റ് പിഎസ്‌സി തുടങ്ങിയ നിങ്ങളുടെ വരാനിരിക്കുന്ന പരീക്ഷകൾക്കായി തയ്യാറെടുക്കുക

Latest Types of Vectors MCQ Objective Questions

Top Types of Vectors MCQ Objective Questions

Types of Vectors Question 1:

If =  =  and  , then angle between  and  is -

  1. π

Answer (Detailed Solution Below)

Option 1 :

Types of Vectors Question 1 Detailed Solution

We Have,

If,  =  = 

⇒ a = b = c .... (1)

And,

 .... (2)

Using the concept of, Parallelogram Law of Vector Addition: It is used to add two vector quantities.

 

R2 = A2 + B2 +2AB cos θ 

From equation (2),

c2 = a2 + b2 +2ab cos θ

Since,

a = b = c

Hence,

a2 = a2 + a2 +2a2 cos θ

or, a2 = a2 (1 + 1 +2cos θ)

or, 1 = 2 + 2 cos θ

or, 2 cos θ = -1

or, cos θ = (-0.5)

Hence, θ = cos-1 (0.5) = 120° = 

Types of Vectors Question 2:

If vectors   then a3 is ?

Where  and  

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

Answer (Detailed Solution Below)

Option 1 : - 2

Types of Vectors Question 2 Detailed Solution

Concept:

Equal Vectors
Two or more vectors are said to be equal when their magnitude is equal and also their direction is the same.

Calculation:

Given:   and   

 

∴ a3 = - 2

Types of Vectors Question 3:

If  ,  and  are such that  is perpendicular to  , then find the value of λ.

  1. 4
  2. 8
  3. 2
  4. -4

Answer (Detailed Solution Below)

Option 2 : 8

Types of Vectors Question 3 Detailed Solution

Concept:

Two vectors  and  are perpendicular if and only if, their dot product is equal to zero.

Solution:

Given:  ,  and 

Then,  

Given that,  is perpendicular to 

Then, 

⇒ 

⇒ 3(2 - λ ) + (2 + 2λ ) = 0 

⇒ 6 - 3λ + 2 + 2λ = 0

⇒ 8 - λ = 0

⇒ λ = 8

∴ The correct option is (2)

Types of Vectors Question 4:

If    and   then a vector in the direction of and having magnitude as is 

Answer (Detailed Solution Below)

Option 4 :

Types of Vectors Question 4 Detailed Solution

Concept:

Vector  of magnitude |p| in the direction of  is given by

​If   then magnitude of ​ is written as​​

Calculation:

Let the required vector is 

A vector in the direction a and magnitude |b| is given by

Hence, option 4 is correct.

Types of Vectors Question 5:

The unit vector which are perpendicular to both the vectors   and  are , 

Answer (Detailed Solution Below)

Option 1 :

Types of Vectors Question 5 Detailed Solution

Concept:

If  perpendicular to both the vectors  and   then 

Unit vector,   

Calculation :

Here the given vectors are,   and  , 

Let, vector  are perpendicular to both the vectors, 

So,   

⇒  

⇒  

∴  =  

Hence the unit vector perpendicular to both the vectors are, 

 =  

⇒  

The correct option is 1. 

Types of Vectors Question 6:

If  is a non-zero vector of modulus a and λ is a non-zero scalar and λ is a unit vector then

  1. λ = ± 1
  2. a = |λ|
  3.  only

Answer (Detailed Solution Below)

Option 3 :

Types of Vectors Question 6 Detailed Solution

Calculation:

 is a non-zero vector of modulus a and λ is a non-zero scalar and  is a unit vector i.e.  = 1

⇒ |λ| = 1   (∵ |mn| = |m|⋅|n|)

⇒ |λ|⋅a = 1   (∵  = a(given))

⇒ a = 

The correct answer is option "3"

Types of Vectors Question 7:

For what value of m are the vector 2î - 3ĵ + 4k̂, î + 2ĵ - k̂ and mî - ĵ + 2k̂ are coplanar ?

  1. 0
  2. 5/3
  3. 1
  4. 8/5

Answer (Detailed Solution Below)

Option 4 : 8/5

Types of Vectors Question 7 Detailed Solution

Concept:

If three vectors a, b and c are coplanar vectors, then

their scalar triple product is zero.

That is, a.(b × c) = 0

Calculation:

Given, 

The vectors 2î - 3ĵ + 4k̂, î + 2ĵ - k̂ and mî - ĵ + 2k̂ are coplanar

⇒  (2î - 3ĵ + 4k̂).[(î + 2ĵ - k̂) × (mî - ĵ + 2k̂)] = 0

⇒  (2î - 3ĵ + 4k̂).[(4  - 1)î - (2 + m)ĵ + (-1 - 2m) k̂] = 0

⇒  (2î - 3ĵ + 4k̂).(3î - (2 + m)ĵ - (1 + 2m) k̂) = 0

⇒  (2)(3) + (-3)(-(2 + m)) + (4)(-(1 + 2m)) = 0

⇒ 6 + 6 + 3m - 4 - 8m = 0

⇒ 8 - 5m = 0

⇒ m = 8/5 

∴ The correct answer is option (4).

Types of Vectors Question 8:

If  are two vectors such that  then which of the following is true ?

  1. a1 = 2, b2 = - 3 and a3 = 1
  2. a1 = - 2, b2 = 3 and a3 = - 1
  3. a1 = 2, b2 = 3 and a3 = 1
  4. a1 = - 2, b2 = 3 and a3 = 1

Answer (Detailed Solution Below)

Option 3 : a1 = 2, b2 = 3 and a3 = 1

Types of Vectors Question 8 Detailed Solution

CONCEPT:

Two vectors are said to be equal if and only if they have same direction and same magnitude.

CALCULATION:

Given:   are two vectors such that 

∵ 

As we know that, two vectors are said to be equal if and only if they have same direction and same magnitude.

So, in order to have same magnitude the corresponding coefficients of  of both the vectors should be same.

⇒ a1 = 2, b2 = 3 and a3 = 1

Hence, option C is the correct answer.

Types of Vectors Question 9:

If the vectors  are collinear and  and |b| = 14, then  is equal to?

  1. None of the above

Answer (Detailed Solution Below)

Option 2 :

Types of Vectors Question 9 Detailed Solution

Concept:

Let 

Magnitude of the vector of a = 

Collinear vectors: Two vectors are collinear if they lie on the same line or parallel lines.

If  and  are collinear vectors then 

Calculation:

Given:

vectors  are collinear,

Therefore, 

⇒ 

Given: magnitude of b = |b| = 14

⇒ 

⇒ 

⇒ 

⇒ 7λ = 14

∴ λ = 2

Now, 

Hence 

Types of Vectors Question 10:

If â, b̂ and ĉ are unit vectors and |â + b̂|2 = |b̂ + ĉ|2 = |ĉ + â|2 = 8, then |2â + b̂ + ĉ| is equal to

  1. 2
  2. 4
  3. 6
  4. none of the above

Answer (Detailed Solution Below)

Option 3 : 6

Types of Vectors Question 10 Detailed Solution

Calculation:

Given,  and    all unit vectors        ---(A)

And

    ---(1)

Take,

1 + 1 + 2 ab = 8 (ab  is unit vector)

2ab = 6

ab = 3

take,

b c = 3

Similarly, c a = 3

Take,

On squaring both sides we get,

 

i.e |2â + b̂ + ĉ| = 6

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