   Chapter 12, Problem 2RCC

Chapter
Section
Textbook Problem

# How do you add two vectors geometrically? How do you add them algebraically?

To determine

To explain: The addition of two vectors geometrically and algebraically.

Explanation

The following are the two laws to illustrate the addition of two vectors geometrically.

• Triangle law
• Parallelogram law

Triangle law:

Consider the two vectors u and v such that the initial position of vector v is the terminal point of vector u.

The sum of two vectors u and v is (u+v). The initial point of vector (u+v) is at the initial point of vector u and the terminal point of vector (u+v) is the terminal point of vector v.

The addition of two vectors using the triangle law is shown in Figure 1.

Parallelogram law:

Consider the two vectors u and v such that the initial position of vector v is the terminal point of vector u.

Draw the vector parallel to the vector u and draw the vector parallel to vector v.

The sum of two vectors u and v is the vector (u+v) or (v+u).

The addition of two vectors using the parallelogram law is shown in Figure 2.

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