   Chapter 1.9, Problem 1.1QQ

Chapter
Section
Textbook Problem

The magnitudes of two vectors A → and B → are 12 units and 8 units, respectively. What are the largest and smallest possible values for the magnitude of the resultant vector R → = A →  +  B → ? (a) 14.4 and 4 (b) 12 and 8 (c) 20 and 4 (d) none of these.

To determine
The largest and smallest possible values for the magnitude of the resultant vector.

Explanation

Given Info: The magnitudes of two vectors A and B are 12 units and 8 units, respectively.

Explanation:

The largest possible value of the resultant vector will occur when the two vectors are in same direction and thus the magnitude of the resultant is the sum of the magnitudes of the two vectors.

Express the resultant vector,

R=(A+B)

Here,

R is the resultant vector

A and B are the vectors

Substitute 12 for A and 8 for B to find the R

R=(12+8)=20unit

The smallest possible value of the resultant vector will occur when the two vectors are in opposite direction and thus the magnitude of the resultant is the difference of the magnitudes of the two vectors

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