Find the unit vector in the same direction as the vector: -3i + 5j.

Answer 1

To find the unit vector v, divide that vector by its magnitude ||v|| = √[(v₁)²+(v₂)²]

v = -3i + 5j = 〈-3,5〉

||v|| = √[(-3)² + (5)²] = √(9+25) = √36 = 6

So the unit vector is 〈-3,5〉/6 = 〈(-3)/6, 5/6〉=〈-1/2, 5/6〉= u

u = -(1/2)i + (5/6)j

Answer 2

Multiply by the scalar 1/norm : in this case 1/ √34. Multiplying by a scalar preserves the direction while multiplying by 1/magnitude ensures the new vector’s magnitude = 1.