Question

Example 4.2 Find the magnitude and
direction of the resultant of two vectors A
and B in terms of their magnitudes and
angle between them.
​

Answer 1

Let the two vectors be represented in magnitude and direction by two adjacent sides OP and OS of parallelogram OPQS, drawn from a point 0.

According to the parallelo gram law of vectors, thier resultant vector R will be

represented by disgnol OQ of the parallelogram.

Manitude of R:

Draw QN perpendicular to OP produced

From the figure, OP=A, OS=PQ = B, OQ = R and SOP = <QPN=6 In AQNP, PN = PQ cose = B cose

QN = PQ sine = B sine In right angled triangle, ONQ, we have

OQ¹ =ON² +NQ¹

=(OP+PN)² +NQ²

or R²= (A + B cose) +(B sine)

or R²=A² + 2AB cose + B² (cos²e+sin³6)

or R²=A¹ +2AB cose+B²

or R= √A +2AB cose + B²