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This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

- Welcome
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- Place Value in Decimal Number Systems
- Arithmetic Operations
- Basic Laws
- Operations on Signed numbers
- Order of Operations
- Some Useful Basic Numeracy
- Decimals
- Fractions
- Percents
- Ratios and Proportions
- Exponents
- Statistics
- Trade and Cash Discounts
- Multiple Rates of Discount
- Payment Terms and Cash Discounts
- Markup
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- Simple Interest
- Equivalent Values
- Compound Interest
- Equivalent Values in Compound Interest
- Nominal and Effective Interest Rates
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- Basic Laws
- Operations with Numbers
- Prime Factorisation and Least Common Multiple
- Fractions
- Exponents
- Reducing Radicals
- Factoring
- Rearranging Formulas
- Solving Linear Equations
- Areas and Volumes of Figures
- Congruence and Similarity
- Functions
- Domain and Range of Functions
- Basics of Graphing
- Transformations
- Graphing Linear Functions
- Graphing Quadratic Functions
- Solving Systems of Linear Equations
- Solving Quadratic Equations
- Solving Higher Degree Equations
- Trigonometry
- Graphing Trigonometric Functions
- Graphing Circles and Ellipses
- Exponential and Logarithmic Functions
- Complex Numbers
- Number Bases in Computer Arithmetic
- Linear Algebra
- Calculus
- Set Theory
- Modular Numbers and Cryptography
- Statistics
- Problem Solving Strategies

- Upgrading / Pre-HealthToggle Dropdown
- Basic Laws
- Place Value in Decimal Number Systems
- Decimals
- Significant Digits
- Prime Factorisation and Least Common Multiple
- Fractions
- Percents
- Ratios and Proportions
- Exponents
- Metric Conversions
- Reducing Radicals
- Factoring
- Solving Linear Equations
- Solving Quadratic Equations
- Polynomial Long Division
- Exponential and Logarithmic Functions
- Statistics

- Nursing MathToggle Dropdown
- Arithmetic Operations
- Place Value in Decimal Number Systems
- Decimals
- Fractions
- Percents
- Ratios and Proportions
- Interpreting Drug Orders
- Oral Dosages
- Dosage Based on Size of the Patient
- Parenteral Dosages
- Intravenous (IV) Administration
- Infusion Rates for Intravenous Piggyback (IVPB) Bag
- General Dosage Rounding Rules

- Transportation MathToggle Dropdown
- Physics

What is a **vector**? A vector is a combination of two quantities, a **magnitude** (an amount), and a **direction**. When written out, they are usually written in bold or with an arrow overtop, so if we have a vector "v", it would be written as "**v**" or "\( \vec{v} \)". We can also perform operations with vectors like addition, subtraction, multiplication, etc. However, this page only covers the basics.

The most common way to see vector quantities written (in 2 dimensions) is with rectangular coordinates, like the regular grid you see in math plots. In rectangular coordinates, we can write our vector, \( \vec{v} \), in terms of its x and y components which we will label \( v_x \) and \( v_y \). The most common forms you'll see are:

**Point form:**\( \vec{v} = (v_x,v_y) \)**Matrix form:**\( \vec{v} = \begin{bmatrix} v_x \\ v_y \end{bmatrix} \)**Unit vector form:**\( \vec{v} = \hat{i} v_x + \hat{j} v_y \) Here, the vector is written in terms of the x and y unit vectors, \( \hat{i} \) and \( \hat{j} \).

These forms are all useful for different types of calculations, however, for basic introductions, point form is the most familiar and intuitive so it will be used for the rest of this help page.

Visually, you can picture this vector like the following image, where \( v_x \) can point anywhere on the x axis and \( v_y \) can point anywhere on the y axis.

In the following graphs, it's important to note that the vector isn't just the end point, it's the whole line.

**Solution:**

Here, our \( v_x = -1\) meaning left 1, and our \( v_y = 2\) meaning up 2, so we would plot \( \vec{v} \) like this:

We can also describe vectors using directions like north, east, south and west. To represent these directions, we can treat the grid of these plots like a compass, so north is the +y direction (up), east is the +x direction (right), south is the -y direction (down), and west is the -x direction (left).

An example of this would be saying "I am traveling 55km/h southward". Here, "-55km/h" would be the magnitude and "southward" would be the direction. To graph a vector given like this, the magnitude represents the length of the arrow and the direction decides where the arrow points. So, if we use the grid like a compass, \( \vec{v} = \) "55km/h southward" would look like this:

It is also worth noting that these vectors are relative to some reference point. With rectangular coordinates, they are relative to the origin point (0,0). On the other hand, the "I am traveling 55km/h southward" example is relative to the north pole because "southward" is a compass direction and compasses use the north pole as a reference point.

As a quick exercise, try drawing the following vectors:

1) \((4,0)\)

2) 14km/h westward

3) \((2,-2)\)

Now, try labeling the following vectors in their rectangular coordinate form:

4)

5)

**Answers:**

1)

2)

3)

4) \( \vec{v} = (2,4) \)

5) \( \vec{v} = (-3,-2) \)

- Last Updated: Feb 1, 2023 2:14 PM
- URL: https://libraryguides.centennialcollege.ca/mathhelp
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