In the Cartesian plane

PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

In the Cartesian plane, a man starts at origin and walks a distance of 3 units of the North-East direction and reaches a point P. From P, he walks a distance of 4 units in the North-West direction to reach a point Q. Construct the parallelogram OPQR with PO and PQ as adjacent sides. Let M be the mid-point of PQ.

Column I	Column II
A. The position vector of P is	(p) $\frac{3}{\sqrt{2}}(\hat{i} + \hat{j})$
B. The position vector of R is	(q) $\frac{1}{\sqrt{2}}(\hat{i} + 5\hat{j})$
C. The position vector of M is	(r) $2\sqrt{2}(-\hat{i} + \hat{j})$
D. If the line OM meets the diagonal PR in the point T, then OT equals	(s) $\frac{\sqrt{2}}{3}(\hat{i} + 5\hat{j})$

Related theory

2D Vectors & Component-wise Representation
Vector Addition & Component Resolution
Scalars and vectors
Addition of vectors
Vector addition (analytical method)
Motion in a Plane

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