Question

Let \[\vec{C} = \vec{A} + \vec{B}\]

Options

• \[\left| \vec{C} \right|\] is always greater than \[\left| \vec{A} \right|\]

• It is possible to have \[\left| \vec{C} \right|\]  < \[\left| \vec{A} \right|\] and \[\left| \vec{C} \right|\] < \[\left| \vec{B} \right|\]

• C is always equal to A + B

• C is never equal to A + B.

Answer 1

It is possible to have \[\left| \vec{C} \right|\]  < \[\left| \vec{A} \right|\] and \[\left| \vec{C} \right|\] < \[\left| \vec{B} \right|\]

Statements (a), (c) and (d) are incorrect.
Given: \[\vec{C} = \vec{A} + \vec{B}\]

Here, the magnitude of the resultant vector may or may not be equal to or less than the magnitudes of \[\vec{A}\] and \[\vec{B}\] or the sum of the magnitudes of both the vectors if the two vectors are in opposite directions.