Alexandra L. answered • 03/15/20
BA in physics with 13 years of experience tutoring math and science
A vector is a line with length and direction. Starting at the origin (0,0) on the Cartesian coordinate plane, the vector <2,7> points two units to the right and seven units up, and so ends at the point (2,7)
We can find the length (magnitude) using the distance formula:
d = √[(x2 - x1)2 + (y2 - y1)2 ]
where (x1, y1) and (x2, y2) are the coordinates of the base and tip of the vector respectively. Selecting (0,0) as the base of the vector simplifies this calculation greatly.
The direction of the vector is given by the angle it makes with the x-axis, when the base of the vector is located at (0,0). The formula for this angle θ is:
θ = tan-1(y2/x2)
