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Chapter 10: Q 27. (page 801)

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

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

Short Answer

Expert verified

The required value ofu+v=3,-8,13andu-v=-1,0,-1.

Step by step solution

01

Step 1. Given information. 

We have given vectoru=1,-4,6andv=2,-4,7.

02

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

u+v=x1+x2,y1+y2,z1+z2=1+2,-4+-4,6+7=3,-8,13andu-v=x1-x2,y1-y2,z1-z2=1-2,-4--4,6-7=-1,0,-1

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

In Exercises 24-27, find compuv,projuvand the component of v orthogonal tou.

u=3,-1,2,v=-4,-6,3

If u and v are nonzero vectors in 鈩�3, why do the equations role="math" localid="1649263352081" u路(u脳v)=0 and v路(u脳v)=0 tell us that the cross product is orthogonal to both u and v?

In Exercises 24-27, find compuv, projuv, and the component of v orthogonal tou.

u=1,2,v=3,5

Find a vector in the direction opposite to-1,-4,-6andwith magnitude 7.

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