**Introduction**

An *equation* is a mathematical expression containing two parts, one on the left-hand side of an equals sign (=) and the other on the right-hand side. A *formula* is an equation used for the purpose of deriving a certain value or solving some practical problem. A *vector* is a special type of quantity in which there are two components: *magnitude* and *direction* . Physics makes use of equations, formulas, and vectors.

**Notation**

Equations and formulas can contain *coefficients* (specific numbers), *constants* (specific quantities represented by letters of the alphabet), and/or *variables* (expressions that stand for numbers but are not specific). Any of the common arithmetic operations can be used in an equation or formula. These include addition, subtraction, multiplication, division, and raising to a power. Sometimes functions are also used, such as logarithmic functions, exponential functions, trigonometric functions, or more sophisticated functions.

Addition is represented by the plus sign (+). Subtraction is represented by the minus sign (−). Multiplication of specific numbers is represented either by a plus sign rotated 45 degrees (×) or by enclosing the numerals in parentheses and writing them one after another. Multiplication involving a coefficient and one or more variables or constants is expressed by writing the coefficient followed by the variables or constants with no symbols in between. Division is represented by a forward slash (/) with the numerator on the left and the denominator on the right. In complicated expressions, a horizontal line is used to denote division, with the numerator on the top and the denominator on the bottom. Exponentiation (raising to a power) is expressed by writing the base value, followed by a superscript indicating the power to which the base is to be raised. Here are some examples:

Two plus three: 2 + 3

Four minus seven: 4 − 7

Two times five: 2 × 5 or (2)(5)

Two times *x: *2 *x*

Two times ( *x* + 4): 2( *x* + 4)

Two divided by *x: *2/ *x*

Two divided by ( *x* + 4): 2/( *x* + 4)

Three to the fourth power: 3 ^{4}

*x* to the fourth power: *x* ^{4}

( *x* + 3) to the fourth power: ( *x* + 3) ^{4}

Practice problems for these concepts can be found at: Equations, Formulas, And Vectors for Physics Practice Test

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