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Prove that $ (a - b) \times (a + b) = 2 (a \times b) $.

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01:25

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 4

The Cross Product

Vectors

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Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

01:35

Prove that $A \cdot(A \tim…

Welcome back to another cross product problem where we're trying to prove an identity involving A minus B. Cross A plus B. We'll break this down into a couple steps. We know that first we can distribute using the cross product and so that this is equivalent to a minus B. Cross A plus A minus B. Cross B. Once again, we can distribute across cross products, meaning this is the same as a cross A minus B. Cross A plus a cross B minus B craft, and we could have done that all in one step, if we wanted to, will notice that any vector across itself is equal to zero and negative be cross A is the same thing as a Crosby. So we have another A Crosby. Any vector cross itself is zero. We're left with a cross B plus a Crosby, which is to a cross B, which is the identity that we wanted to show. Thanks for what.

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