The Cross Product of Vectors | How to Use a 3x3 Matrix Determinant

In this advanced physics and further mathematics tutorial, we break down Multiplication of Vectors Part 2: The Cross Product (Vector Product) from the absolute ground up. While the dot product results in a scalar, the cross product produces a completely new vector that stands perfectly perpendicular to both original vectors. Mastering this operation is vital for solving problems involving torque, angular momentum, and magnetic fields. We walk you through this advanced vector algebra workspace step-by-step: The Core Definition (The Vector Product): Understanding why the direction of a cross product is governed by the Right-Hand Rule. We introduce the geometric formula: A x B = |A| |B| sin(theta) n-hat, where n-hat is the unit vector pointing perpendicular to the plane. The Cyclic Unit Vector Rules: Revealing how unit vectors cross each other. We show you the simple visual circle trick to remember why: i x j = k j x k = i k x i = j We also show you why reversing the order flips the sign (j x i = -k), proving that the cross product is non-commutative. Derivation via the 3x3 Matrix Determinant: The ultimate foolproof method for your exams! We build a 3x3 matrix where: Row 1 contains the unit directional basis vectors: [i, j, k] Row 2 contains the components of the first vector: [ax, ay, az] Row 3 contains the components of the second vector: [bx, by, bz] Solving the 3x3 Determinant Step-by-Step: We break the large 3x3 matrix down into three smaller 2x2 determinants using the standard sign pattern (Positive i, Negative j, Positive k). We explicitly show you how to cross-multiply the terms so you never make a careless sign error under exam pressure. Authentic Exam Past Questions: Detailed, step-by-step solutions to tricky past examination questions where you are required to compute the cross product of two 3D vectors or find a vector perpendicular to a given plane. This video directly aligns with universal advanced physics and further mathematics standards taught in Senior Secondary Schools, Class 12, A-Level Mathematics, WAEC/WASSCE, NECO, JAMB UTME, Post-UTME, and introductory College Physics and Engineering courses. It serves as an invaluable, highly targeted revision resource for science students sitting for competitive entrance examinations worldwide. 🎓 Welcome to Excellent Link Academy! I'm Ganiyu Abubakar, an educator, content creator, and founder of Excellent Link Academy. On this channel, you'll find educational tutorials, academic success strategies, science lessons, YouTube growth tips, digital skills training, and much more. ━━━━━━━━━━━━━━━━━━━━ ⭐ JOIN VIP MEMBERSHIP Get access to exclusive content, special tutorials, member-only benefits, and premium resources:    / @excellentlinkacademyofficial   ━━━━━━━━━━━━━━━━━━━━ 🌐 VISIT MY OFFICIAL WEBSITE Access courses, study materials, and educational resources: https://www.ganiyuabubakar.com ━━━━━━━━━━━━━━━━━━━━ 📚 GET MY BOOK "The Shortcut to Academic Success" https://selar.com/aa84051788 ━━━━━━━━━━━━━━━━━━━━ 📱 JOIN MY WHATSAPP CHANNEL Get updates, study tips, and exclusive content: https://whatsapp.com/channel/0029Vb5h... ━━━━━━━━━━━━━━━━━━━━ 👨‍🏫 NEED A PRIVATE TUTOR? Send a WhatsApp message: +2349123155603 ━━━━━━━━━━━━━━━━━━━━ 👥 JOIN OUR OFFICIAL WHATSAPP GROUP https://chat.whatsapp.com/BHFYO4RtFsv... ━━━━━━━━━━━━━━━━━━━━ 🎵 FOLLOW ME ON TIKTOK   / excellentlinkacademy   📸 FOLLOW ME ON INSTAGRAM   / ganiyu_abubakar_   ━━━━━━━━━━━━━━━━━━━━ 🔔 Subscribe and turn on notifications so you never miss a new upload! #ganiyuabubakar #excellentlinkacademy #education #onlinelearning #scienceeducation #academicsuccess #studytips #physics #chemistry #youtubegrowth #digitalSkills #mathematics #ganiyuabubakar #excellentlinkacademy #ganiyuabubakar #excellentlinkacademy #ganiyuabubakar #excellentlinkacademy #ganiyuabubakar #excellentlinkacademy #ganiyuabubakar #excellentlinkacademy #ganiyuabubakar #excellentlinkacademy