/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 71 Draw two vectors, \(\mathbf{v}\)... [FREE SOLUTION] | 91影视

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Chapter 6: Problem 71

Draw two vectors, \(\mathbf{v}\) and \(\mathbf{w},\) with the same initial point. Show the vector projection of \(\mathbf{v}\) onto \(\mathbf{w}\) in your diagram. Then describe how you identified this vector.

Short Answer

Expert verified
The vector projection of \( \mathbf{v} \) onto \( \mathbf{w} \) is the component of \( \mathbf{v} \) that lies in the direction of \( \mathbf{w} \), which is showed in the diagram as a segment of \( \mathbf{w} \) starting from the initial point.

Step by step solution

01

Draw vectors

Draw two vectors \( \mathbf{v} \) and \( \mathbf{w} \) with the same initial point. These vectors can be drawn as arrows pointing outwards from the same point, with their length and direction representing their magnitude and direction respectively.
02

Understand Vector Projection

The projection of one vector onto another is a vector that is parallel to the second vector and has the length of the component of the first vector in the direction of the second.
03

Draw the Projection

To show the projection of \( \mathbf{v} \) onto \( \mathbf{w} \), draw a line perpendicular to \( \mathbf{w} \) that passes through the tip of \( \mathbf{v} \). The projection is the portion of \( \mathbf{w} \) that lies between the initial point of both vectors and the point where the perpendicular line meets \( \mathbf{w} \).
04

Identification of the projection vector

The vector drawn alongside \( \mathbf{w} \), and passing through the initial point is the projection vector of \( \mathbf{v} \) onto \( \mathbf{w} \). The vector is easily identifiable as it lies along \( \mathbf{w} \) and starts from the same initial point as \( \mathbf{v} \) and \( \mathbf{w} \).

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Most popular questions from this chapter

Determine whether v and w are parallel, orthogonal, or neither. $$\mathbf{v}=-2 \mathbf{i}+3 \mathbf{j}, \quad \mathbf{w}=-6 \mathbf{i}-4 \mathbf{j}$$

A force is given by the vector \(\mathbf{F}=5 \mathbf{i}+7 \mathbf{j} .\) The force moves an object along a straight line from the point (8,11) to the point \((18,20) .\) Find the work done if the distance is measured in meters and the force is measured in newtons.

Will help you prepare for the material covered in the next section. Use slope to determine if the line through (-3,-3) and (0. 3) is parallel to the line through ( 0.0 ) and (3,6)

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Let $$\mathbf{u}=-\mathbf{i}+\mathbf{j}, \quad \mathbf{v}=3 \mathbf{i}-2 \mathbf{j}, \quad \text { and } \quad \mathbf{w}=-5 \mathbf{j}$$ Find each specified scalar or vector. $$5 \mathbf{u} \cdot(3 \mathbf{v}-4 \mathbf{w})$$
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