Question

Fin a unit vector from the point (2,2) toward (6,5):

Answer 1

To find a unit vector from point A(2,2) to point B(6,5), we first need to find the vector from A to B. This is done by subtracting the coordinates of A from the coordinates of B:

AB = (6-2, 5-2) = (4,3)

Next, we find the magnitude (length) of this vector using the Pythagorean theorem:

|AB| = sqrt((4)^2 + (3)^2) = 5

Finally, we divide each component of the vector AB by its magnitude to get the unit vector in the direction of AB:

AB_unit = (4/5, 3/5)

So, the unit vector from point (2,2) toward (6,5) is (4/5, 3/5). This vector has a length of 1 and points in the direction of AB.