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 unitless 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 â€“ 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.

__Question and Answers__

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

- \(3\hat{i}+2\hat{j}+5\hat{k}\)
- \(3\hat{i}-2\hat{j}-5\hat{k}\)
- \(5\hat{i}+2\hat{j}+3\hat{k}\)
- \(2\hat{i}+5\hat{j}+3\hat{k}\)

**Answer: **(a)** **\(3\hat{i}+2\hat{j}+5\hat{k}\)

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

- \(\hat{i}+\hat{j}+5\hat{k}\)
- \(2\hat{i}+4\hat{j}+6\hat{k}\)
- \(\hat{i}+\hat{j}\)
- \(\hat{i}+\hat{j}10\hat{k}\)

**Answer: **(c)** **\(\hat{i}+\hat{j}\)

3. What is the vertical component of the force 5 N acting on a particle along a direction making an angle of 60^{0}?

- 3 N
- 2.5 N
- 10 N
- 4 N

**Answer: **(b) 2.5 N

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

- \(\frac{2}{\sqrt{45}},\frac{4}{\sqrt{45}}, -\frac{5}{\sqrt{45}}\)
- \(\frac{4}{\sqrt{45}},0, -\frac{4}{\sqrt{45}}\)
- \(\frac{3}{\sqrt{45}},\frac{2}{\sqrt{45}}, \frac{5}{\sqrt{45}}\)
- \(\frac{1}{\sqrt{45}},\frac{2}{\sqrt{45}}, \frac{5}{\sqrt{45}}\)

**Answer: **(a)** **\(\frac{2}{\sqrt{45}},\frac{4}{\sqrt{45}}, -\frac{5}{\sqrt{45}}\)

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

- 1
- 2
- 3
- 4

**Answer: **(c) 3

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

- 17 m
- 20 m
- 26 m
- 36 m

**Answer: **(b) 20 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?

- 10 N
- \(10\sqrt{2}\,N\)
- 20 N
- 0

**Answer:** (d) 0

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

- perpendicular to each other and have the original vector as their resultant
- Parallel to each other and have the original vector as their resultant
- Arbitrary vectors which have original vectors as their resultant
- It is impossible to resolve a vector

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

**9.** Angular momentum is

- A scalar vector
- An axial-vector
- A polar vector
- A displacement vector

**Answer:** (b)** **An axial-vector

10. Which of the following is a vector?

- Surface Tension
- Moment of Inertia
- Pressure
- None of the above

**Answer: **(d) None of the above

11. Which of the following is a scalar quantity?

- Acceleration
- Electric Field
- Work
- Displacement

**Answer: **(d) Displacement

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

- His displacement is 700 m
- His displacement is 500 m
- He has travelled a distance of 700 m
- His velocity is not uniform throughout the walk

**Answer:** (b) His displacement is 500 m

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