Question

Find a unit vector that has the same direction as the given vector. 8, −32

Answer 1

To find a unit vector that has the same direction as a given vector, divide each component of the vector by its magnitude.

Step-by-step explanation:

To find a unit vector that has the same direction as a given vector, we need to divide the given vector by its magnitude. In this case, the given vector is (8, -32). The magnitude of this vector can be found using the Pythagorean theorem:

|v| = sqrt((8^2) + (-32^2)) = sqrt(64 + 1024) = sqrt(1088) ≈ 32.98

Now, we can find the unit vector by dividing each component of the given vector by its magnitude:

Unit vector = (8/32.98, -32/32.98) ≈ (0.242, -0.970)