Question

(i)	Position vector $\overrightarrow{A}$	(1)	$2\hat{i}+\hat{j}$
(ii)	Postion vector $\overrightarrow{B}$	(2)	$3\hat{i}+3\hat{j}$
(iii)	Displacement ${\overrightarrow{d}}_{AB}$	(3)	$5\hat{i}+4\hat{j}$
(iv)	Position vector of point of intersection of path 1 & path 2	(4)	$4\hat{i}+3\hat{j}$

• A. (i) - (3), (ii) - (1), (iii) - (2), (iv) - (4)
• B. (i) - (2), (ii) - (3), (iii) - (1), (iv) - (4)
• C. (i) - (1), (ii) - (2), (iii) - (3), (iv) - (4)
• D. (i) - (4), (ii) - (1), (iii) - (3), (iv) - (2)

Answer 1

The correct option is A

(i) - (3), (ii) - (1), (iii) - (2), (iv) - (4)

(i) From the diagram, you can see that A is at (5,4). $\therefore$ position vector is $5\hat{i}+4\hat{j}$.
(ii) Similarly, B is $2\hat{i}+\hat{j}$.
(iii) ${\overrightarrow{d}}_{AB}$ is the displacement vector if you move from B to A. $\therefore {\overrightarrow{d}}_{AB}=\overrightarrow{A}-\overrightarrow{B}$
$=5\hat{i}+4\hat{j}-(2\hat{i}+\hat{j})$
$=3\hat{i}+3\hat{j}$
You can also see that if you shift the origin to B, the position vector of A becomes, $3\hat{i}+3\hat{j}$.
(iv) Point of intersection is at $4\hat{i}+3\hat{j}$