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Chapter 10: Q. 9 (page 800)

How do you add two vectors algebraically? Geometrically

Short Answer

Expert verified

u=x1i+y1jandv=x2i+y2ju鈫�+v鈫�=x1+x2i+(y1+y2)

Step by step solution

01

Addition of vectors algebraically

If two vectors u鈫�andv鈫�are given,

u=x1i+y1jandv=x2i+y2ju鈫�+v鈫�=x1+x2i+(y1-y2)

Example:

u鈫�=3i+8jandv鈫�=2i-4ju鈫�+v鈫�=3i+2i+8j-4j=5i+4j

02

Addition of vectors geometrically

Let,

u鈫�=3i+8jandv鈫�=2i-4ju鈫�+v鈫�=3i+2i+8j-4j=5i+4j

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Most popular questions from this chapter

Suppose f and g are functions such that limx鈫�3f(x)=5,limx鈫�4f(x)=2andlimx鈫�3g(x)=4

Given this information, calcuate the limits that follow, if possible. If it is not possible with the given information, explain why.

limx鈫�3-2f(x)

Find vand find the unit vector in the direction of v.

v=3,鈭�4

In Exercises 37鈥�42, find v and find the unit vector in the direction of v.

v=15,13

Suppose that we know the reciprocal rule for limits: If limx鈫�cg(x)=Mexists and is nonzero, then limx鈫�c1g(x)=1MThis limit rule is tedious to prove and we do not include it here. Use the reciprocal rule and the product rule for limits to prove the quotient rule for limits.

Calculate each of the limits:

limh鈫�011+h-1h.
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