The Dot Product, Multivariable Calculus

(Unit 1 Lecture 07) The dot product: how to compute it, properties, relationship to the angle between two vectors, a.b=0 if and only if a and b are perpendicular, a vector is perpendicular to a plane. We begin by defining the dot product and its computation in various dimensions, emphasizing its applicability in spaces like R2, R3, and beyond. A significant focus is placed on the geometric interpretation of the dot product, particularly in determining the angle between vectors and identifying orthogonal vectors.

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