Let A = 4i - 2j, B = -3i + 5j, and C = A + B. (c) What are the magnitude and director of vector C?

Video transcript

Hey everyone. So this problem is working with vector addition. Let's see what they're asking us given two vectors M equals six, I minus four J and N equals negative five I plus two J. We are asked to find the magnitude and direction of calculator calculated vector P where P equals M plus N. So our multiple choice answers here are a 2. at an angle of 63.4 degrees above the positive X axis B 2.24 at an angle of 63.4 degrees below the positive X axis C 9.0 at an angle of 30 degrees above the positive X axis or D 2.24 at an angle of 27 degrees below the positive X axis. So because they are asking us to find the magnitude and direction of the vector, we are first going to find the component form and then use trigonometry to find that magnitude and direction. So let's get into it. You've got vector P is equal to vector M plus vector N. And so we're going to add the I and J components of those vectors together to find vector P in component form. So vector P equals six I plus negative five I and then vector and then the jade direction, the J terms excuse me R negative four J from the M vector and then positive two J from vector N. OK. So we can simplify this and we are left with I minus two J. And so from here, we can recall that the magnitude of the vector is the square root of the sum of squares. And so that looks like P equals square root of one squared plus negative two squared. And that comes out to 2.24. And then when we have uh the opposite and adjacent sides of a hypotenuse that tells us to use tangent from Sakata. So tangent of theta equals the opposite over the adjacent. And in our case, that means that beta equals the inverse tangent of negative 2 over that equals negative 63.4°. So because that is negative, that tells us that the angle is below the positive X axis. So our magnitude is 2.24 and our angle is 63.4 degrees below the positive X axis. So that aligns with answer choice B. So that's all we have for this one. We'll see you in the next video.