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Chapter 10: Q 40. (page 801)

In Exercises 37–42, find vand find the unit vector in the direction of v.

v=2,1,-5

Short Answer

Expert verified

v=30 and the unit vector in the direction of vis 1302,1,-5.

Step by step solution

01

Step 1. Given information.

The given vector is:

v=2,1,-5

02

Step 2. Find the norm of the vector.

v=2,1,-5v=22+12+52=4+1+25=30

Therefore, the norm of the given vector is30.

03

Step 3. Find the unit vector in the direction of v.

The unit vector in the direction of vis the vector:

1vv=1302,1,-5

Therefore, the unit vector in the direction ofv=2,1,-5is1302,1,-5.

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Most popular questions from this chapter

What is meant by the parallelogram determined by vectors u and v in ℝ3? How do you find the area of this parallelogram?

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The sum formulas in Theorem 4.4 can be applied only to sums whose starting index value is k=1.

(b) True or False: ∑k=0n 1k+1+∑k=1n k2is equal to ∑k=0n k3+k2+1k+1.

(c) True or False: ∑k=1n 1k+1+∑k=0n k2is equal to ∑k=1n k3+k2+1k+1 .

(d) True or False: ∑k=1n 1k+1∑k=1n k2 is equal to ∑k=1n k2k+1.

(e) True or False: ∑k=0m k+∑k=mn kis equal to∑k=0n k.

(f) True or False: ∑k=0n ak=−a0−an+∑k=1n−1 ak.

(g) True or False: ∑k=110 ak2=∑k=110 ak2.

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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(1,4,6),Q(−3,5,0),R(3,2,−1)

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

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

Find a vector of length 3 that points in the direction opposite to1,-2,3.
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