Vectors - Math is Fun
Velocity, acceleration, force and many other things are vectors. Subtracting. We can also subtract one vector from another: first we reverse the direction of the vector we want to subtract, then add them as usual: a − b. Notation. A vector is often written in bold, like a or b.
Vector Calculator - Math is Fun
Enter values into Magnitude and Angle ... or X and Y. It will do conversions and sum up the vectors. Learn about Vectors and Dot Products.
Eigenvector and Eigenvalue - Math is Fun
If v is non-zero then we can (hopefully) solve for λ using just the determinant: | A − λI | = 0. Let's try that equation on our previous example:
Cross Product - Math is Fun
The Cross Product a × b of two vectors is another vector that is at right angles to both: And it all happens in 3 dimensions! The magnitude (length) of the cross product equals the area of a parallelogram with vectors a and b for sides:
Solving Systems of Linear Equations Using Matrices - Math is Fun
We went on to solve it using "elimination", but we can also solve it using Matrices! Using Matrices makes life easier because we can use a computer program (such as the Matrix Calculator ) to do all the "number crunching".
Dot Product - Math is Fun
Here are two vectors: They can be multiplied using the "Dot Product" (also see Cross Product). Calculating. The Dot Product is written using a central dot: a · b This means the Dot Product of a and b. We can calculate the Dot Product of two vectors this way: a · b = |a| × |b| × cos(θ) Where: |a| is the magnitude (length) of vector a
Unit Vector - Math is Fun
Unit vectors can be used in 2 dimensions: Here we show that the vector a is made up of 2 "x" unit vectors and 1.3 "y" unit vectors. In 3 Dimensions. Likewise we can use unit vectors in three (or more!) dimensions: Advanced topic: arranged like this the three unit vectors form a basis of 3D space. But that is not the only way to do this!
Polar and Cartesian Coordinates - Math is Fun
When we know a point in Cartesian Coordinates (x,y) and we want it in Polar Coordinates (r,θ) we solve a right triangle with two known sides. Example: What is (12,5) in Polar Coordinates? Use Pythagoras Theorem to find the long side (the hypotenuse):
Parallel and Perpendicular Lines - Math is Fun
We can solve it by using the "point-slope" equation of a line: y − y 1 = 2(x − x 1) And then put in the point (5,4): y − 4 = 2(x − 5) That is an answer! But it might look better in y = mx + b form. Let's expand 2(x − 5) and then rearrange: y − 4 = 2x − 10. y = 2x − 6
Force Calculations - Math is Fun
We can use trigonometry to solve it. Because it is a right-angled triangle, SOHCAHTOA will help. For the Beam, we know the Adjacent, we want to know the Opposite, and "TOA" tells us to use Tangent: tan(60°) = Beam/785 N. Beam/785 N = tan(60°) Beam = tan(60°) × 785 N. Beam = 1.732... × 785 N = 1360 N