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
Latest Types of Vectors MCQ Objective Questions
Top Types of Vectors MCQ Objective Questions
Types of Vectors Question 1:
If
Answer (Detailed Solution Below)
Types of Vectors Question 1 Detailed Solution
We Have,
If,
⇒ a = b = c .... (1)
And,
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
Where
Answer (Detailed Solution Below)
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:
∴ a3 = - 2
Types of Vectors Question 3:
If
Answer (Detailed Solution Below)
Types of Vectors Question 3 Detailed Solution
Concept:
Two vectors
Solution:
Given:
Then,
Given that,
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
Answer (Detailed Solution Below)
Types of Vectors Question 4 Detailed Solution
Concept:
Vector
If
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
Answer (Detailed Solution Below)
Types of Vectors Question 5 Detailed Solution
Concept:
If
Unit vector,
Calculation :
Here the given vectors are,
Let, vector
So,
⇒
⇒
∴
Hence the unit vector perpendicular to both the vectors are,
⇒
The correct option is 1.
Types of Vectors Question 6:
If
Answer (Detailed Solution Below)
Types of Vectors Question 6 Detailed Solution
Calculation:
⇒ |λ|
⇒ |λ|⋅a = 1 (∵
⇒ 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 ?
Answer (Detailed Solution Below)
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
Answer (Detailed Solution Below)
Types of Vectors Question 8 Detailed Solution
CONCEPT:
Two vectors
CALCULATION:
Given:
∵
As we know that, two vectors
So, in order to have same magnitude the corresponding coefficients of
⇒ a1 = 2, b2 = 3 and a3 = 1
Hence, option C is the correct answer.
Types of Vectors Question 9:
If the vectors
Answer (Detailed Solution Below)
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
Calculation:
Given:
vectors
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
Answer (Detailed Solution Below)
Types of Vectors Question 10 Detailed Solution
Calculation:
Given,
And
Take,
1 + 1 + 2 ab = 8 (ab
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