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
Answer (Detailed Solution Below)
Magnitude and Directions of a Vector Question 1 Detailed Solution
Concept:
Magnitude of vector
Calculation:
Given: Let
⇒
As we know that, if
⇒ |
⇒
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 ______.
Answer (Detailed Solution Below)
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
then the vector equation of the line passing through A and B is given by I
Calculation:
Let the position vector of points A (-1, 0, 2) and B (3, 4, 6) be
Then,
And,
⇒
⇒ I
⇒ I
⇒ I
∴ 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)
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
Answer (Detailed Solution Below)
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
Answer (Detailed Solution Below)
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?
Answer (Detailed Solution Below)
Magnitude and Directions of a Vector Question 6 Detailed Solution
Download Solution PDFConcept:
Let
Calculation:
Let
Given,
⇒
⇒
⇒ 3p = 3
∴ p = 1
If A =
Answer (Detailed Solution Below)
Magnitude and Directions of a Vector Question 7 Detailed Solution
Download Solution PDFConcept:
If
Calculation:
Given A =
Now
If
Answer (Detailed Solution Below)
Magnitude and Directions of a Vector Question 8 Detailed Solution
Download Solution PDFConcept:
The magnitude of a vector
The magnitude of the sum of vectors
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
Now,
What is the value of k for which the vector k(2î - ĵ - 2k̂) is of 6 units length?
Answer (Detailed Solution Below)
Magnitude and Directions of a Vector Question 9 Detailed Solution
Download Solution PDFConcept:
Length of the vector
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
Answer (Detailed Solution Below)
Magnitude and Directions of a Vector Question 10 Detailed Solution
Download Solution PDFCONCEPT:
If
CALCULATION:
Given:
Here, we have to find the value of
⇒
As we know that, if
⇒
Hence, option D is the correct answer.
Find the direction cosines of the vector 7î + 4ĵ - 3k̂.
Answer (Detailed Solution Below)
Magnitude and Directions of a Vector Question 11 Detailed Solution
Download Solution PDFConcept:
The direction cosines of the vector aî + bĵ + ck̂ are given by α =
Calculation:
For the given vector 7î + 4ĵ - 3k̂, a = 7, b = 4 and c = -3.
The direction cosines of the vector are:
α =
⇒ α =
∴ (α , β , γ ) = (
Answer (Detailed Solution Below)
Magnitude and Directions of a Vector Question 12 Detailed Solution
Download Solution PDFConcept:
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,
If the position vectors of points A and B are
Answer (Detailed Solution Below)
Magnitude and Directions of a Vector Question 13 Detailed Solution
Download Solution PDFConcept:
If A and B are points with position vectors
If
Calculation:
Given: The position vectors of points A and B are
As we know, If A and B are points with position vectors
As we know that, If
What are the values of x for which the angle between the vectors 2x2
Answer (Detailed Solution Below)
Magnitude and Directions of a Vector Question 14 Detailed Solution
Download Solution PDFConcept:
- 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
The angle between the vectors 2x2
⇒
⇒
Since θ is obtuse,
⇒ cos θ < 0
⇒ 3x2 - 6x < 0
⇒ x(x - 2) < 0
⇒ 0 < x < 2
∴ The correct option is (1).
Answer (Detailed Solution Below)
Magnitude and Directions of a Vector Question 15 Detailed Solution
Download Solution PDFGiven:
Calculation:
We have,
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒
Put the value of
⇒
⇒
∴