For v=4i-8j, find unit vector u in the direction of v

a. u = 1/3i - 2/3j

b. i-j

c. sqrt3/3 i - 2 sqrt3/3 j

d. sqrt5/5 i - 2 sqrt5/5 j

The unit vector is given by:

u = v / lvl

The module of v is:

lvl = root ((4) ^ 2 + (-8) ^ 2)

lvl = root (16 + 64)

lvl = root (80)

lvl = 4 * root (5)

Substituting:

u = 4i-8j / (4 * root (5))

Rewriting:

u = i-2j / root (5)

u = root (5) / 5 i - 2 * root (5) / 5 j

Answer:

The unit vector in the direction of v is:

d. sqrt5 / 5 i - 2 sqrt5 / 5 j