Let v=-3√2i-4√2j. Find a unit vector that points in the opposite direction as v.

Question

Let v=-3√2i-4√2j. Find a unit vector that points in the opposite direction as v.

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

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

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

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

Answer 1

Let v=-3√2i-4√2j

The vector with the same magnitude but opposite to v (let's call it u vector) is:

_ _

u = 3√2 i + 4√2 j. (we simply change the sign of each term).

However, this is not a unit vector and we can check it by getting the value of || u ||:

_{_______________}

|| u || = √(3√2)² + (4√2)²

_{_______________}

|| u || = √(9*2) + (16*2)

_{________ ___ __}

|| u || = √ 18 + 32 = √ 50 = 5√ 2 (Since || u || is not equal to one, this is not a unit vector)

To get the unit vector opposite to v is:

_{__ __}

u / || u || = 3√2 i + 4√2 j = (3/5) i + (4/5)j

5√ 2