ANSWER
Step-by-step explanation
First, let us make a sketch of the vectors:
The thick black line represents the vector sum of the two vectors A and B.
We see that the coordinates of the vector (A + B) are:
We can write it in component form as:
To find the magnitude of (A + B), we have to find the length of the line using the formula:
where (x, y) are the coordinates of the vector.
Hence, the magnitude of the vector is:
To find the direction of the vector (A + B), we have to apply the formula:
Therefore, the direction of the vector is:
Since the vector is in the fourth quadrant, then, the direction is:
Therefore, the magnitude and direction of the sum vector (A + B) are: