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Two vectors vec(A) and vec(B) are added....

Two vectors `vec(A)` and `vec(B)` are added. Prove that the magnitude of the resultant vector cannot be greater than `(A+B)` and smaller than `(A-B)` or `(B-A)`.

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To prove that the magnitude of the resultant vector \( \vec{R} \) from two vectors \( \vec{A} \) and \( \vec{B} \) cannot be greater than \( A + B \) and cannot be smaller than \( A - B \) or \( B - A \), we can follow these steps: ### Step 1: Understand the Resultant of Two Vectors The resultant vector \( \vec{R} \) when two vectors \( \vec{A} \) and \( \vec{B} \) are added can be calculated using the formula: \[ R = \sqrt{A^2 + B^2 + 2AB \cos \theta} \] where \( \theta \) is the angle between the two vectors. ...
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