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

Answer 1

Hi Vi,

A unit vector is just a vector with a magnitude of one. So all you need to do for this question is find the direction of the vector -3i+5j. In fact, i indicates a unit vector pointing in the positive x-direction and j a unit vector pointing to the positive y-direction. The numbers -3 and 5 indicate those vector's magnitudes.

I always find it useful to draw pictures when I'm dealing with vectors. It makes it very clear that adding the vectors -3i and 5j and then drawing their sum will result in a right triangle. You can then use trig to figure out the direction and magnitude of that vector.

Now if a unit vector is just a vector with a magnitude of 1, we can find a specific unit vector by dividing the vector by its own magnitude, that is, -3/mag i + 5/mag j. You will find that the occurring vector will be at the same angle as its original but only have a magnitude of 1 unit.

I hope that helps! Please let me know if you have any other questions.