MATH 32A Lecture Notes - Lecture 4: Multivariable Calculus, Cross Product, Quadrilateral

• School: UCLA
• Department: Mathematics
• Course: MATH 32A
• Professor: Austin, A.D.

Document Summary

Lecture 4: cross product and applications, functions and graphs in. How to compute the cross product of 2 3-d vectors v and w: In the first row, the numbers are i, j, and k (the special unit vectors for 3-d vectors). In the second row, in order, are the x, y, and z-components of vector v, and in third row are the components of w. Then, the cross product of v and w (v x w) is the determinant of this matrix. Geometric meaning of the cross product: note that since v x w is a vector, and vectors have magnitude and direction, in order to describe v x w geometrically, we need to describe both magnitude and direction. Direction of v x w is perpendicular (orthogonal) to both v and w. The direction your thumb is pointing to is the direction of v x w. Theta is the angle between the two vectors.