Pre Calculus

Question

Let v= -3√2 i- 4√2 j. Find a unit vector that points in the opposite direction as v.
a)5/3i + 5/4j

b)-3/5i - 4/5j

c) -5/3i - 5/4j

d) 3/5i + 4/5j

 

Answer 1

Your vector lies in Quadrant III, so its opposite would lie in Quadrant I, so b and c are eliminated right off the bat.  

 

Next, answer d is a unit vector, as required, as 3:4:5 is a Pythagorean triple, so you don't even have to do the calculation.  Both components of vector a are greater than 1, so vector a cannot be a unit vector.

 

If you actually want to calculate the answer (or want to confirm the result) the reference angle for the Quadrant III vector is Arctan 4/3, which is the same as the Arctan for answer d.