The magnitudes of displacements overrightarrow (a) and overrightarrow (b) are 3 m and 4 m, respectively and overrightarrow (c)=overrightarrow (a)+overrightarrow (b) . Considering various orientations of overrightarrow (a) and overrightarrow (b) what are (a) the maximum possible magnitude for overrightarrow (c) and (b) the minimum possible magnitude?

Question

Answer 1

To find the maximum and minimum possible magnitudes of the vector

, we need to consider the different orientations of

and

.(a) Maximum possible magnitude:The maximum possible magnitude of

occurs when the vectors

and

are aligned in the same direction. In this case, the magnitudes of

and

can be added directly.Maximum magnitude of

= magnitude of

+ magnitude of

= 3 m + 4 m = 7 m.(b) Minimum possible magnitude:The minimum possible magnitude of

occurs when the vectors

and

are perpendicular to each other. In this case, the magnitudes of

and

can be subtracted using the Pythagorean theorem.Minimum magnitude of

=

= 5 m.Therefore, the maximum possible magnitude of

is 7 m, and the minimum possible magnitude is 5 m.

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