Vector A ＝ 3î＋ĵ and vector B＝ 3î ─ 2ĵ ＋ 2k. What is the cross product A ✕ B?

Video transcript

Hey, everyone. So this problem is working with vector cross products. We are asked to find the cross product of C cross D. When the given vectors are C equals two, I plus three J and D equals I minus four, J plus five K. Our multiple choice answers here are a 15, I -10, J -11 K B 15, I minus J C 10, I plus 10, J minus five K or D -3 I -2 J Plus K. So to find the cross product, we are going to write the determinant using the magnitude of each component. So that looks like in our eye for the eye components, we have two from our C vector and one from our D vector. Same for the J, we have three and then negative four from our D vector. So we carry, we keep this um sign while we are writing our determinant. So this is negative form. And then in the K, the K components, there is no K component in vector C. So that will be zero and then it is positive five. And for vector D, so for our I components, so C cross D is equal to, for our eye, we have three 04 and five for that matrix. So, and so J cross K four hour J direction I cross K is negative. So we're gonna say negative or minus J and then R I is two and one K is zero and five and then K is equal to I cross J and that's positive. So plus K, that matrix looks like two, 1, 3 and -4. So we'll solve this deter these determinants. So C cross D is equal to 15, I will cross multiply. So three times five is 15 and then zero times four is zero. The J we have minus J again, two times five is 10, 1 times zero is zero. And then for K, we have negative eight minus three which simplifies to -11. So C cross D equals 15, I minus 10, 10 J minus 11 K. So that is the final answer for this problem. And that aligns with answer choice A so A is the correct answer. That's all we have for this one. We'll see you in the next video.