Question

Let v1=(2,-6) and v2=(-4,7)

Answer 1

The magnitude of each vector is the Pythagorean sum of its components.

a. |v1| = √(2² + (-6)²) = √40 = 2√10

|v2| = √((-4)² + 7²) = √65

b. To make each vector into a unit vector, divide each component by the vector's magnitude.

u1 = v1/|v1| = (2/(2√10), -6/(2√10))

u1 = (√10/10, -3√10/10)

u2 = v2/|v2| = (-4/√65, 7/√65)

u2 = (-4√65/65, 7√65/65)