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For the vectors in Exercise 40, find $ orth_a b $ and illustrate by drawing the vectors $ a, b, proj_a b, $ and $ orth_a b $.

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$\operatorname{orth}_{\mathrm{a}} \mathrm{b}=\left\langle\frac{20}{17},-\frac{5}{17}\right\rangle$

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.

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For the vectors in Exercis…

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The problem is for the vectors in exercise 40 flying to work to solving production of b, unto a and illustrated by drawing the vectors of b, a b projection of b unto a and solving projection of b into a so first in exercise 40, we have vector A is equal to 1 hund 4 vector b is equal to 23 point, so the work to projection of b into a is equal to a dot b over its magnitude of a square times, as this is equal to 14 over 17 times 14 point. So this is equal to 14 over 17 and 56 over 17 and a soganaprojuction of b unto a is equal to vector b minus projection of b into a pot. This is equal to 2 or 3 minus 14 over 1756. Over 17 point. This is equal to 20 over 17 and negative 5 over 17. Now we can jot the lectors a projection of b into a and solving projection of b unto a as follows. This point is this: trouai minus 4 and b is 2, a is 23 and it's a projection of b into a is likethe fluger and a southern projection of b into a is this 1 over half. This looks like a sapona 2 vector a.

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