Let A = 4i - 2j, B = -3i + 5j, and F = A - 4B. (a) Write vector F in component form.

Video transcript

Hey, everyone. So this problem is working with vectors. Let's see what they're asking us, evaluate the vector operation R equals M minus five N where M equals five, I minus three J and N equals negative two I plus J expressing the result in components. So they're giving us two vectors in component form and asking us to solve for it in component form. Our multiple choice answers are a negative five J minus sorry, negative five J plus two JB 15, I plus eight J C 15, I minus eight J four D 5.39, I plus 3.16 J. OK. So we know we're solving for vector R which equals M -5. And, and we already are given to us directly in the problem which equals 5 I -3 J and we need five, multiplied by N. So vector N is negative two I plus J and we can multiply the five by both sides through to get the value of 5 n. So that will be negative 10, I plus five J. And so now we can solve or R we will take the I components first and then the J components. So R equals M minus five N. So in the I components, that's five I minus negative I plus the J components. So that will be negative three J from M and then plus five J from five N. Oops, sorry. So it'll be -5 J because it is M -5 n. So -3 J -5 J. There we go. Or the J components. And so we simplify that through and we are left with 15 I -8 J and they ask for it in component form. So we don't need to do anything else to, so to solve for this problem, we look at our multiple choice answers and that aligns with answer choice C. All right, that's all we have for this one. We'll see you in the next video.