Chapter 12.6, Problem 6LC

Solution

To find: To explain why the statement is incorrect.

The magnitudes of the vectors cannot be compared by individual components of the vector.

Given information:

Given, a friend says that the magnitude of vector $〈8,3〉$ is 4 times that of the vector $〈2,3〉$ since 8 is 4 times 2.

Calculation:

The magnitude of a vector $〈a,b〉$ is given by $\sqrt{a^2+b^2}$

The magnitude of the vector $〈8,3〉$ is $\sqrt{8^2+3^2}=\sqrt{64+9}=\sqrt{73}$

The magnitude of the vector $〈2,3〉$ is $\sqrt{2^2+3^2}=\sqrt{4+9}=\sqrt{13}$

Hence the friend’s statement is incorrect.

The magnitudes of the vectors cannot be compared by individual components of the vector but only by calculating the magnitudes.

Conclusion:

The magnitudes of the vectors cannot be compared by individual components of the vector.