Vectors

First identify the X and Y components of your vectors.

In most every case this will be the horizontal distance of the vector (X)

And the vertical distance of the vector (Y)

Then you add together both the X's and both the Y's

Subtraction is the same as addition but you need to reverse the second vector in the operation.

If the question asks for (7,8), you need to reverse the second vector and do addition as normal.

The question ten becomes (7,8) + (9,-10)

Solving that gets you (19,-2)

Magnitude of vectors is found using pythagoras theorem

Sqrt(x^2+8^2)

So for the vector (5,8)

Sqrt (5^2+8^2)

Start with the squares Sqrt (89)

Then the square root 9.43398113206

There are a few ways to multiply vectors

Scalar

Dot product

Cross product

Scalar Multiplication

Scalar multiplication is when we are asked to multiply a vector by a single number (the scalar)

You multiply your vectors co-ordinates by the scalar number

This looks like 6x(7,8) which would equal (42,48)

Dot Product

Dot product can be done in two ways depending on whether you have the co-ordinates or the magnitude and angle for your vectors

Dot Product (with co-ords)

This method works in a similar way to addition

We multiply the matching co-ordinates and then add the results

The formula looks like (Ax * Bx)+(Ay * By)

So for A= (10,11) and B= (12,13)

We would have (10*12) + (11*13)= 120+143=263

Dot Product (with magnitude)

When working with magnitude and angle we use a different formula

The magnitude of A times the magnitude of B x the cosine of the angle of 60 between them

We would do 10*13* cos(60)= 65

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