Vector a is 5.5cm long and points along the x-axis. vector b is 7.5cm long and points at +30 degrees above the negative x axis.

a. determine the x and y components of vector a and vector b
b. determine the sum of these two vectors in terms of components.
c. determine the sum of these two vectors in terms of magnitude and direction

a)

b)

c)

Step-by-step explanation:

If we call A and B the longitude of the vectors, and measure from the positive x axis in anti-clockwise direction (as usual), the x and y components are determined by the formulas:

An angle of 30 degrees above the negative x axis is an angle of 180-30=150 degrees from the positive x axis in anti-clockwise direction. So we will have:

The sum of the 2 vectors (each of the components of their sum) in terms of their components will be:

Since and are the sides of a right triangle, the magnitude of the sum of A+B (which we will call |A+B|) will be given by the Pythagoras formula, and the angle can be calculated with the formula of the arc tangent since :

For the angle one has to be careful since the arctan function cannot interpret some results. In our case, the vector A+B is on Quadrant II (negative x, positive y), so the best way will be to calculate the angle above negative x (using the absolute values of the components), and to 180 substract this value, then:

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step-by-step explanation: