Cross Product of 2 Vectors (How to Find)

Описание: Learn how to find the cross product of two vectors with this step-by-step tutorial! Mario's Math Tutoring guides you through two examples, demonstrating the determinant method using standard unit vectors (i, j, k). Understand the right-hand rule to visualize the direction of the resulting vector, and learn how to verify that the cross product is orthogonal (perpendicular) to both original vectors using the dot product.

In this video, you'll discover:

0:00 Introduction to the Cross Product of Two Vectors
0:20 Visualizing the Cross Product with the Right-Hand Rule
1:00 Understanding the Direction and Perpendicularity of the Resulting Vector
1:30 Importance of Order (U x V vs. V x U)
2:00 Setting Up the Cross Product as a 3x3 Determinant (Method of Minors)
2:20 Standard Unit Vectors (i, j, k)
2:50 The Determinant Formula (i - j + k)
3:20 Calculating the Minor Matrices
4:10 Calculating the Determinant of 2x2 Matrices
5:00 Example 1: Finding U x V for U = (3, 1, 4) and V = (-2, 2, -3)
6:00 Writing the Cross Product in Component Form
6:10 Verifying Orthogonality with the Dot Product (Dot Product = 0)
7:30 Example 2: Finding U x V for U = (-3, 5, 1) and V = (-2, -3, 4)
8:00 Setting Up the Determinant for Example 2
9:00 Calculating the Determinants and Simplifying
10:10 Verifying Orthogonality for Example 2
Master the cross product of vectors and confidently solve problems in multivariable calculus and physics!

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