Precalculus: Find unit vector

Question

FInd unit vector.

a) v= -5i + 12j

b) v= i-j

Answer 1

A unit vector is defined as a vector that has a magnitude of 1. To calculate the unit vector, we use the following formula:

u = v / ||v||

where v is a vector and ||v|| is the magnitude of the vector given by:

||v|| = √(x_i² + y_j²)

for case a:

||v|| = √((-5)² + (12)²) = √169 = 13

u = (-5i + 12j) / 13 = (-5/13)*i + (12/13)*j

for case b:

||v|| = √((1)² + (-1)²) = √2 ≈ 1.414

u = (i - j) / 1.414 = (1/1.414)*i + (-1/1.414)*j