Which of the following conditions is true for equal vectors? 2. What is the magnitude of a vector that makes an angle of 30° to the horizontal and whose x-component is 3 units? 3. Which one of the fol

The x-component of a vector $\vec{A}$ is given by $A_x = A \cos \theta$, where $A$ is the magnitude of the vector and $\theta$ is the angle it makes with the horizontal.
Given: $A_x = 3$ units, $\theta = 30^\circ$.

To rationalize the denominator, multiply the numerator and denominator by $\sqrt{3}$:

• The closest option is C.
• Answer: C. 3.46 units

3. Which one of the following represents a scalar quantity?
A scalar quantity has only magnitude, while a vector quantity has both magnitude and direction.

• A. Change in momentum is a vector.
• B. Velocity is a vector.
• C. Speed is a scalar.
• D. Acceleration is a vector.
• The correct option is C.
• Answer: C. The speed of a car travelling at 100 km/h.

4. Which of the following groups consists only of vectors?
A vector quantity has both magnitude and direction.

• A. Pressure is a scalar.
• B. Momentum, force, and velocity are all vectors.
• C. Speed is a scalar.
• D. Temperature is a scalar.
• The correct option is B.
• Answer: B. Momentum, force, velocity

5. What is vector resolution?
Vector resolution is the process of breaking down a single vector into its perpendicular components, typically along the x and y axes.

• The correct option is B.
• Answer: B. Breaking a vector into its components along the coordinate axes.

6. If a vector has a magnitude of 10 units and makes a $30^\circ$ angle with the horizontal, what is the magnitude of its vertical component?

The vertical component of a vector $\vec{A}$ is given by $A_y = A \sin \theta$, where $A$ is the magnitude of the vector and $\theta$ is the angle it makes with the horizontal.
Given: $A = 10$ units, $\theta = 30^\circ$.

• The correct option is A.
• Answer: A. 5 units

7. A vector is resolved into components along the x and y axes. What is true about the components?
The magnitudes of the components ($A_x = A \cos \theta$ and $A_y = A \sin \theta$) depend directly on the angle the vector makes with the axes. They are not always equal, nor is one always larger than the other, and they are certainly not independent of the vector's direction.

• The correct option is B.
• Answer: B. They are dependent on the angle made by the vector with the axes.

8. Which of the following pairs of components would correctly resolve a vector of magnitude 15 units making a $45^\circ$ angle with the horizontal?

Given: $A = 15$ units, $\theta = 45^\circ$.
The x-component is $A_x = A \cos \theta$.
The y-component is $A_y = A \sin \theta$.

• The correct option is B.
• Answer: B. 10.6 units along x, 10.6 units along y

9. What is the first step in the graphical method of vector addition?
The graphical method of vector addition involves drawing vectors to scale. The very first step is to represent each vector accurately with its correct magnitude and direction.

• The correct option is B.
• Answer: B. Draw vectors to scale with appropriate directions.