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A vector is anything with magnitude and direction. A magnitude is simply a numerical value. If I'm traveling north at 43 m/s, then "43 m/s" is the magnitude, and north is the direction.
Typically, vectors are drawn as simply rays. The vector begins at the base and ends at the tip of the arrowhead. The length of the vector indicates its magnitude, while its direction is...well...the direction it's pointing.
Often, the direction can be determined and reported as the angle above the horizontal or the angle above the positive x-axis. This can be found simply by drawing an imaginary horizontal line starting at the base of the vector.
Important note: it's impossible for a ray with "negative" length to be drawn. When dealing with vectors, a negative number simply indicates that the vector is now pointing in the exact opposite direction - 180 degrees from its original direction.
A physical property that has magnitude but NO direction is called a scalar. An example of this is mass - if I have a mass of 70 kg, that's it. I'm not dealing with 70 kg to the right, left, up, or down - just 70 kg. Examples of scalars include energy, time (sort of), mass, electrical charge, and more.
vector components
vector components
Before you can start to understand vectors and vector components, you need a solid grasp of right triangle trigonometry. Specifically, soh cah toa:
In this image, the angle θ is labeled. Assume the sides labeled "opposite," "adjacent," and "hypotenuse" all have values associated with them. The relationships between the angle's value and its corresponding sides are as follows:
Sin(θ) = opposite/hypotenuse
Cos(θ) = adjacent/hypotenuse
Tan(θ) = opposite/adjacent
...Don't forget that you can use inverse trig functions to solve for θ itself!
Once you have a strong grasp of soh cah toa, you can use it to break vectors down into more manageable pieces.
Once you have a strong grasp of soh cah toa, you can use it to break vectors down into more manageable pieces.
As mentioned previously, you can identify a vector by its magnitude and direction, but that's not all - you can also break it into its x and y components - "x" being horizontal and "y" being vertical. See the video below for an explanation as to how that works.
Now that you know how to break down a vector into its components, you can use those components to add vectors together. This skill will be crucial when we get into forces and free body diagrams, so make sure you see me for extra practice now if you need it! See the video below for a vector addition walkthrough.
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