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Chapter 10: Q 50. (page 801)

Find a unit vector in the direction opposite to3,4,5.

Short Answer

Expert verified

The required vector is150-3,-4,-5.

Step by step solution

01

Step 1. Given information.

The given vector is:

v=3,4,5

02

Step 2. Find the norm of the vector.

v=3,4,5v=32+42+52=9+16+25=50

Therefore, the norm of the given vector is 50.

03

Step 3. Find the vector.

We know that the vector in the direction of vis 1v-v. Here ais the magnitude of the given vector and the negative sign shows the direction opposite tov=3,4,5.

The required vector is:

role="math" localid="1649521227299" 1vv=150-3,4,5=150-3,-4,-5


Therefore, the unit vector in the direction opposite to v=3,4,5is150-3,-4,-5.

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Most popular questions from this chapter

If u, v, and ware three mutually orthogonal vectors in 鈩�3, explain why u脳(v脳w)=0.

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(3,1,8),Q(0,6,鈭�1),R(鈭�3,5,鈭�3)

If u and v are vectors in 鈩�3 such that u路v=0 and u脳v=0, what can we conclude about u and v?

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: 鈭�k=0n鈥�1k+1+鈭�k=1n鈥�k2is equal to 鈭�k=0n鈥�k3+k2+1k+1.

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

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

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

(f) True or False: 鈭�k=0n鈥�ak=鈭�a0鈭�an+鈭�k=1n鈭�1鈥�ak.

(g) True or False: 鈭�k=110鈥�ak2=鈭�k=110鈥�ak2.

(h) True or False: 鈭�k=1n鈥�ex2=exex+12ex+16.

Find u+vandu-valso sketch u,v,u+v,u-v

role="math" localid="1649603034674" u=1,-4,6andv=2,-4,7
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