Question

$A$ moves from a point $P(1,2,3)$ to point $Q(4,6,8)$. In which one of the following cases the displacement vector is same as that of $A$?

• A. $B$ moves from $R(2,3,5)$ to $S(1,2,3)$
• B. $C$ moves from $T(7,8,5)$ to $U(4,4,0)$.
• C. $D$ moves from $V(1,2,5)$ to $W(4,6,10)$
• D. $E$ moves from $X(0,0,0)$ to $Y(1,2,3)$.

Answer 1

The correct option is C $D$ moves from $V(1,2,5)$ to $W(4,6,10)$

The displacement vector is the difference between the final position and the initial position.
So, displacement of $A$ is
$\overrightarrow{S_A}=(4\hat{i}+6\hat{j}+8\hat{k})-(1\hat{i}+2\hat{j}+3\hat{k})$
$=3\hat{i}+4\hat{j}+5\hat{k}$
Similarly, from the options, the displacement of $B,C,D$ and $E$ is
$\overrightarrow{S_B}=(1\hat{i}+2\hat{j}+3\hat{k})-(2\hat{i}+3\hat{j}+5\hat{k})$
$=-1\hat{i}+-1\hat{j}-2\hat{k}$
$\overrightarrow{S_C}=(4\hat{i}+4\hat{j}+0\hat{k})-(7\hat{i}+8\hat{j}+5\hat{k})$
$=-3\hat{i}-4\hat{j}-5\hat{k}$
$\overrightarrow{S_D}=(4\hat{i}+6\hat{j}+10\hat{k})-(1\hat{i}+2\hat{j}+5\hat{k})$
$=3\hat{i}+4\hat{j}+5\hat{k}$
$\overrightarrow{S_E}=(1\hat{i}+2\hat{j}+3\hat{k})-(0\hat{i}+0\hat{j}+0\hat{k})$
$=1\hat{i}+2\hat{j}+3\hat{k}$
$\because \overrightarrow{S_A}=\overrightarrow{S_D}$
Hence, option (C) is correct.