Find a unit vector that points in the opposite direction as v.

Question

Find a unit vector that points in the opposite direction as v.

 

Let .v=-3(pi 2)i-4(pi 2)j

 

A. u= (3/5)i+(4/5)j

B. u= -(3/5)i-(4/5)j

C. u= -(5/3)i-(5/4)j

D. u= (5/3)i+(5/4)j

 

Answer 1

v = (-3π/2)i -(4π/2)j

 

ll v ll = √ [ (-3π/2)² + (-4π/2)² ] = π √ (25/4) = 5π/2

 

A unit vector in the opposite direction to v is:

 

    u = -v/(ll v ll) = (2/(5π))[(3π/2)i + (4π/2)j]

 

                        = (3/5)i +(4/5)j   (Answer is A)