Find the component form and the magnitude of the vector v In

Find the component form and the magnitude of the vector v. Initial Point (-2, 14) Terminal Point (6, 40)

Solution

Solution:

If the vector has an initial point (x1, y1) and terminal point (x2, y2), then the vector is given by ( x2 - x1, y2 - y1 ).

So in this case, the vector is ( 6 - (-2) , 40 - 14) = (8, 26).

component form, v = i8 -j26

The magnitude or length or \"norm\" of a vector (x,y) is given by
sqrt ( x^2 + y^2).
So in this case, the magnitude = sqrt( 8^2 + 26^2) =
sqrt( 64 + 676) = sqrt( 740 ) which is approx 27.20

magnitude v = 27.20
component form, v = i8 -j26