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Chapter 10: Q 26. (page 801)

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

u=4,0andv=0,3

Short Answer

Expert verified

The required value ofu+v=4,3andu-v=4,-3.

Step by step solution

01

Step 1. Given information.  

We have given vectoru=4,0andv=0,3.

02

Step 2. Find the values of u+v and u-v.

u+v=x1+x2,y1+y2=4+0,0+3=4,3

and

u-v=x1-x2,y1-y2=4-0,0-3=4,-3

03

Step 3. Sketch u, v, u+v and u-v.

The graph of vector u+v.

The graph of vector u-v.

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Most popular questions from this chapter

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?

Consider the function f shown in the graph next at the right. Use the graph to make a rough estimate of the average value of f on [鈭�4, 4], and illustrate this average value as a height on the graph.

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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.

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.)
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