Question

How does the resultant displacement change as the angle between two vectors increases from 90° to 120°?



A. None of these are correct.
B. The resultant decreases.
C. The resultant increases.
D. The resultant stays the same magnitude, but its direction changes.

Answer 1

The resultant displacement between the two vectors will increase.

The resultant of the two vectors is given by parallelogram law of vectors.

The parallelogram law of vector addition states that if two vectors are represented in magnitude and direction by the adjacent sides of a parallelogram, the diagonal of the parallelogram drawn from the point of intersection of the vectors represents the resultant vector in magnitude and direction.

The resultant of these vectors, say vector A, and B, is given as;

$R^2 = a^2 + b^2 -2ab.Cos (\theta )$

When;

θ = 90°

$R^2 = a^2 + b^2$

When;

θ = 120°

$R^2 = a^2 + b^2 + ab$

Thus, the resultant displacement between the two vectors will increase.

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