INSTRUCTOR: Let vector a equal, angle bracket, 16, comma, negative 11, angle bracket. And let vector b be a unit vector that forms an angle of 225 degrees with the positive x-axis. Express vector a and vector b in terms of the standard unit vectors. Well, vector a will simply be equal to 16i minus 11j, because we could write that as 16 multiplied by the vector 1, 0. That's i.

Minus 11 multiplied by the vector 0, 1, which is the j vector. So there is a in standard unit vector notation. Now, for angle-- not an angle, the vector. Vector b, we know that we can write this as the magnitude of the vector.

So I'm just going to write this. It's magnitude of vector b multiplied by cosine of 225 degrees plus the magnitude of b multiplied by the sine of 225 degrees. And I just need to add an i and a j in here, so let me read that off again. The magnitude of vector b times cosine 225 degrees i plus the magnitude of b times sine of 225 degrees j. That would be it in standard unit vector notation.

Well, we know that, since b is a unit vector, the magnitude of b is equal to 1. And using some trigonometry, we know the cosine of 225 degrees is equal to negative square root of 2 over 2. And sine of 225 degrees is negative square root of 2 over 2 as well. If it helps, remember that 225 degrees is in the third quadrant. It's in the third quadrant, and it would have a reference angle with the negative x-axis of 45 degrees. That's what I use to calculate those, so perhaps that's useful.

Now, putting all that together, that means that vector b is equal to 1 times negative square root of 2 over 2. So it is negative square root of 2 over 2i minus square root of 2 over 2j. That is that vector in standard unit vector notation.