Vector a s is 3.00 units in length and points along the positive x - axis. vector b s is 4.00 units in length and points along the negative y - axis. use graphical methods to find the magnitude and direction of the vectors (a) a s 1 b s and (b) a s 2 b s .

Answers:

a) Magnitude:5 units  Direction: or South of East

b) Magnitude:5 units  Direction: or North of East

Explanation:

Vectors in two dimensions have two components Y and X, and are written in the following form:

(X,Y)

In this case we have two vectors:

We need to find and , their magnitude and direction.

For the magnitude we will use the formula to calculate the distance between two points (pithagorean theorem):

(1)

For the direction, which is the measure of the angle the vector makes with a horizontal line, we will use the following formula:  

(2)

Now, let's begin with the answers:

a)

Adding both vectors:

Finding the magnitude:

This is the magnitude of  

Finding the direction:

This is the direction of  

If we assume the positive x axis as the East and the negative y axis as the South, we can also express this direction as:

South of East

b)

Substracting to :

Finding the magnitude:

This is the magnitude of  

Finding the direction:

This is the direction of  

If we assume the positive x axis as the East and the positivr y axis as the North, we can also express this direction as:

North of East

gravity

explanation: