   Chapter 1, Problem 15CQ

Chapter
Section
Textbook Problem

If B → is added to A → , under what conditions does the resultant vector have a magnitude equal to A + B? Under what conditions is the resultant vector equal to zero?

To determine
The condition for resultant vector to be A+B and the condition for resultant vector to be 0.

Explanation

The direction of vectors A and B plays an important role in determining the resultant vector to be A+B.

Formula for resultant of two vectors is

R=|A|2+|B|2+2|A||B|cosθ (I)

Here,

θ is the angle between two vectors

When θ is 0°, the right hand side of Equation (1) is A+B.

The condition is that A and B should be parallel.

Both the direction and magnitude of vectors A and B is significant in determining the resultant vector to be a null vector

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