NEET MCQs-Fundamentals of Vectors

A vector is a quantity that has both direction and magnitude. Vectors are divided into two types as polar vectors and axial vectors. A vector having a unit magnitude is called a unit vector. A unit vector is dimensionless and unit less and only represents direction.

Triangle Law of Vectors

If two vectors acting at a point are represented in magnitude and direction by the two sides of a triangle taken in one order, then their resultant is represented by the third side of the triangle taken in the opposite order.

Parallelogram Law of Vectors

If two vectors acting at a point are represented in magnitude and direction by the two adjacent sides of a parallelogram drawn from a point, then their resultant is represented in magnitude and direction by the diagonal of the parallelogram drawn from the same point.

Polygon Law of Vectors

The law states that if a number of vectors acting on a particle at a time is represented in magnitude and – direction by the various sides of an open polygon taken in the same order, their resultant vector E is represented in magnitude and direction by the closing side of a polygon taken in the opposite order.

Questions and Answers

1. The position of a particle in a rectangular coordinate system is (3,2,5). What will the position vector be?

1. \(\begin{array}{l}3\hat{i}+2\hat{j}+5\hat{k}\end{array} \)
2. \(\begin{array}{l}3\hat{i}-2\hat{j}-5\hat{k}\end{array} \)
3. \(\begin{array}{l}5\hat{i}+2\hat{j}+3\hat{k}\end{array} \)
4. \(\begin{array}{l}2\hat{i}+5\hat{j}+3\hat{k}\end{array} \)

Answer: (a)

\(\begin{array}{l}3\hat{i}+2\hat{j}+5\hat{k}\end{array} \)

2. What is the displacement vector of the particle that moves from point P (2,3,5) to point Q (3,4,5)?

1. \(\begin{array}{l}\hat{i}+\hat{j}+5\hat{k}\end{array} \)
2. \(\begin{array}{l}2\hat{i}+4\hat{j}+6\hat{k}\end{array} \)
3. \(\begin{array}{l}\hat{i}+\hat{j}\end{array} \)
4. \(\begin{array}{l}\hat{i}+\hat{j}10\hat{k}\end{array} \)

Answer: (c)

\(\begin{array}{l}\hat{i}+\hat{j}\end{array} \)

3. What is the vertical component of the force 5 N acting on a particle along a direction making an angle of 60⁰?

1. 3 N
2. 2.5 N
3. 10 N
4. 4 N

Answer: (b) 2.5 N

\(\begin{array}{l}4. \ What \ is \ the \ direction \ of \ cosines \ of \ vector \ \vec{A} = 2\hat{i}+4\hat{j}-5\hat{k}?\end{array} \)

1. \(\begin{array}{l}\frac{2}{\sqrt{45}},\frac{4}{\sqrt{45}}, -\frac{5}{\sqrt{45}}\end{array} \)
2. \(\begin{array}{l}\frac{4}{\sqrt{45}},0, -\frac{4}{\sqrt{45}}\end{array} \)
3. \(\begin{array}{l}\frac{3}{\sqrt{45}},\frac{2}{\sqrt{45}}, \frac{5}{\sqrt{45}}\end{array} \)
4. \(\begin{array}{l}\frac{1}{\sqrt{45}},\frac{2}{\sqrt{45}}, \frac{5}{\sqrt{45}}\end{array} \)

Answer: (a)

\(\begin{array}{l}\frac{2}{\sqrt{45}},\frac{4}{\sqrt{45}}, -\frac{5}{\sqrt{45}}\end{array} \)

5. What is the minimum number of coplanar vectors with different magnitudes that can be added to get a resultant of zero?

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

Answer: (c) 3

6. A fly in the hall of dimensions 10 m×12 m×14 m starts to fly from one corner and ends up at the diametrically opposite corner. What is the magnitude of its flight?

1. 17 m
2. 21 m
3. 26 m
4. 36 m

Answer: (b) 21 m

7. Five equal forces of 10 N are applied at a point. If the angle between them is equal, what is the resultant force?

1. 10 N
2. \(\begin{array}{l}10\sqrt{2}\,N\end{array} \)
3. 20 N
4. 0

Answer: (d) 0

8. Any vector in an arbitrary direction can be replaced by two or three vectors

1. perpendicular to each other and have the original vector as their resultant
2. Parallel to each other and have the original vector as their resultant
3. Arbitrary vectors which have original vectors as their resultant
4. It is impossible to resolve a vector

Answer: (c) Arbitrary vectors which have original vectors as their resultant

9. Angular momentum is

1. A scalar vector
2. An axial-vector
3. A polar vector
4. A displacement vector

Answer: (b) An axial-vector

10. Which of the following is a vector?

1. Surface Tension
2. Moment of Inertia
3. Pressure
4. None of the above

Answer: (d) None of the above

11. Which of the following is a scalar quantity?

1. Acceleration
2. Electric Field
3. Work
4. Displacement

Answer: (c) Work

12. A boy walks uniformly along the sides of a rectangular park with dimensions 400 m×300 m, starting from one corner to the other corner diagonally opposite. Which of the following statements is false?

1. His displacement is 700 m
2. His displacement is 500 m
3. He has travelled a distance of 700 m
4. His velocity is not uniform throughout the walk

Answer: (a) His displacement is 700 m