A5 newton force and a 7 newton force act concurrently on a point. as the angle between the forces is increased from 0 to 180 the magnitude of the resultant of the two forces changes from

The resultant of the two vectors when the angle between them is increased from 0 to 180 is 12 N.

The given parameters;

The resultant of the two vectors will be determined using parallelogram rule as shown below;

where;

R² = (5)² + (7)²  -  (2 x 5 x 7) cos(180)

R² = 74 - (-70)

R² = 74 + 70

R² = 144

R = √144

R = 12 N

Thus, the resultant of the two vectors when the angle between them is increased from 0 to 180 is 12 N.

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The magnitude of the resultant decreases from A+B to A-B

Explanation:

The magnitude of the resultant of two vectors is given by

where

A is the magnitude of the first vector

B is the magnitude of the second vector

is the angle between the directions of the two vectors

In the formula, A and B are constant, so the behaviour depends only on the function . The value of are:

- 1 (maximum) when the angle is 0, so the magnitude of the resultant in this case is

- then it decreases, until it becomes 0 when the angle is 90 degrees, where the magnitude of the resultant is

- then it becomes negative, and continues to decrease, until it reaches a value of -1 when the angle is 180 degrees, and the magnitude of the resultant is

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