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Q 49.

Expert-verified
Calculus
Found in: Page 801
Calculus

Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Illustration

Short Answer

Find a vector in the direction opposite to 0,-3,4 and with magnitude 10.

The required vector is 20,3,-4.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1. Given information.

The given vector is:

v=0,-3,4 with magnitude 10.

Step 2. Find the norm of the vector.

v=0,-3,4v=02+-32+42=0+9+16=25=5

Therefore, the norm of the given vector is 5.

Step 3. Find the vector.

We know that the vector in the direction of v is av(-v). Here a is the magnitude of the given vector and the negative sign shows the direction opposite to v=0,-3,4.

The required vector is:

localid="1649520584341" av-v=105-0,-3,4=20,3,-4

Therefore the vector in the direction opposite to v=0,-3,4 and with a magnitude of 10 is 20,3,-4.

Most popular questions for Math Textbooks

If u and v are nonzero vectors in ℝ3, why do the equations role="math" localid="1649263352081" u·(u×v)=0 and v·(u×v)=0 tell us that the cross product is orthogonal to both u and v?

Find PQ→.

P = (3, 6), Q = (−3, −2)

In Exercises 30–35 compute the indicated quantities when u=(−3,1,−4), v=(2,0,5), and w=(1,3,13)

role="math" localid="1649434688557" v×w and w×v

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

u=2,0,-5, v=-3,7,-1

In Exercises 36–41 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,−2), Q(−2,0), R(1,−5)

(Hint: Think of the xy-plane as part of ℝ3.)
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