Distance And Displacement MCQ - NEET Practice Questions with Answers

1. Position vector

• The location of a point, in space, is an important physical quantity that is also known as a position vector.

• Representation of position vector

$\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}$

• Its magnitude is the distance between the initial point (tail) and the final point (head). 

(Generally, we take the initial point as the origin)

• Its direction is from the initial point and the final point. 

Magnitude of $r=\sqrt{x^2+y^2+z^2}$

$$
\begin{aligned}
& \text { - E.g. If } \vec{A}=3 \hat{i}-4 \hat{j}+2 \hat{k}_{\text {then its magnitude }} \\
& =\sqrt{(3)^2+(-4)^2+(2)^2} \\
& =\sqrt{9+16+4} \\
& a=\sqrt{29}
\end{aligned}
$$
 

2. Distance or Path length

• Length of actual path between the initial and final positions of the body.

• E.g. Distance traveled along a circle for one complete rotation is $2 \pi r$

• Tips of distance

1. Distance is a scalar quantity.

2. It is always positive.

3. S.I. Unit $\rightarrow$ meter (m).
   Dimension $[L]$

4. Distance depends on the path followed by body.  

3. Displacement

• The shortest path is between the initial and final position.

• Tips for Displacement.

1. Displacement is a vector quantity.

2. It can be positive, zero or negative.

3. Displacement is independent of the path.

4. 4. S.I. unit $\rightarrow$ Meter (m)
    Dimension (L)
    Displacement $\leqslant$ Distance.
   - E.g. For Semi circle

   Distance $=\pi r$ while Displacement $=2 r$