Scalars And Vectors - Practice Questions & MCQ

1. Scalars

Physical quantities can be described completely by their magnitude only but no particular direction.

Examples- Distance, speed, work, charges, temperature, etc.

Tips for scalars-

• Scalar quantities can be positive, negative or zero.

• Represented by alphabet only A, B, C.

• These physical quantities follow normal algebraic rules of addition.

2.  Vectors

Physical quantities can be described by their magnitude and direction.

Physical quantities like Displacement, force, velocity etc. are vectors.

Tips of vectors-

• Vectors can be positive, negative or zero.

• Represented by alphabet having an arrow on their head.

         $\overrightarrow{A},\overrightarrow{B},\overrightarrow{C}$

•   These physical quantities follow the laws of vector addition.

•  Types of vectors

1.  Equal vectors-

            Two vectors are said to be equal if they have equal magnitude and the same directions.

$\begin{array}{rl}& ⟶\overrightarrow{A}\\ & ⟶\overrightarrow{B}\\ & \overrightarrow{A}=\overrightarrow{B}\end{array}$

The angle between these two vectors $\mathrm{\Theta }$ is equal to zero.

2. Negative vectors-

              Two vectors are said to be negative with respect to each other if they have equal magnitude but opposite directions.

$\begin{array}{rl}& \to \overrightarrow{A}\\ & \leftarrow \overrightarrow{B}\\ & \overrightarrow{A}=-\overrightarrow{B}\end{array}$

The angle between negative vectors is equal to 180 . i.e $\mathrm{\Theta }={180}^{\circ }$
3. Collinear vectors-

Two vectors are said to be collinear if they have a common line of action.
a. If two vectors are collinear and parallel then the angle between them is zero.
b. If two vectors are collinear and anti-parallel then the angle between them is ${180}^{\circ }$.

So, Angle between collinear vectors A \& B is either zero or ${180}^{\circ }$.

$\text{ i.e; }\mathrm{\Theta }=0^{\circ }\text{ or }{180}^{\circ }$
 

4. Co-initial vectors-

                Two vectors are said to be Co-initial vectors if they have the same initial point.