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Find $ a \cdot b $.

$ a = \langle p, -p, 2p \rangle $ , $ b = \langle 2q, q, -q \rangle $

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$-p q$

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot 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.

01:03

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01:10

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00:30

Solve.$$q=\frac{p+…

01:59

Given $P(A \bar{B})=\frac{…

00:59

Solve.$p-q=q r s,$ for…

01:11

$$p+q=p q$$

Solve for the indicated va…

00:37

Give the formula for findi…

okay to find the doc product here we multiply component wise and at the moment. Okay, so this one's with variables, but it's totally fine.

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