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Chapter 10: Q. 21 (page 801)

What is the set of all position vectors in \(R^3\) of magnitude \(5\)?

Short Answer

Expert verified

It is the set of all the position vectors whose terminal points are on the sphere with a radius of \(5\) and a center at the origin.

Step by step solution

01

Step 1. Given Information

All position vectors in \(R^3\) with magnitude \(5\).

02

Step 2. Find the set of position vectors

Consider the following graph

The graph shows the vector with a magnitude of \(5\).

The set of all position vectors in \(R^3\) with magnitude \(5\) is the set of all the position vectors whose terminal points are on the sphere with radius \(5\) and center at the origin.

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Most popular questions from this chapter

Find PQ鈬赌

P=5,-3,Q=3,-6

If u and v are vectors in 鈩�3 such that u脳v=v脳u, what can we conclude about u and v?

Find u+vand u-v. Also sketchu,v,u+vand u-v.

role="math" localid="1649578020551" u=3,-4andv=-1,5

In Exercises 36鈥�41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(4,鈭�2),Q(鈭�2,0),R(1,鈭�5)

(Hint: Think of the xy-plane as part of 鈩�3.)

In Exercises 36鈥�41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(4,3,鈭�2),Q(0,0,3),R(鈭�1,3,6)
See all solutions

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