Q. 19

Question

How do you generalize the ideas of this section to vectors with four components? To vectors with n components?

Step-by-Step Solution

Verified

Answer

If there are two vectors u and v in four components such that $u = <x_{1}, y_{1}, z_{1}, w_{1}>$ and $v = <x_{2}, y_{2}, z_{2}, w_{2}>$ $v = <m, n, o, p>$ , then the two vectors will be added component-wise.

1Step 1: Given information

Let two vectors u and v in four components such that $u = <x_{1}, y_{1}, z_{1}, w_{1}>$ and $v = <x_{2}, y_{2}, z_{2}, w_{2}>$

2Step 2: Adding the vectors with four and 'n' components.

To add the two vectors with four components, add the component as follows.

$u + v = <x_{1} + x_{2}, y_{1} + y_{2}, z_{1} + z_{2}, w_{1} + w_{2}> u + v = <x_{1} + x_{2} + . . . . + x_{n}, y_{1} + y_{2} + . . . + y_{n}, z_{1} + z_{2} + . . . . + z_{n}, w_{1} + w_{2} + . . . . + w_{n}>$

Q. 18

Q. 20

Other exercises in this chapter

Q. 17

Let v0=(a, b, c) and let v=(x, y, z) Describe the sets of points in R3 satisfying the following properties:(a). v=4(b).&

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Q. 18

Let $v=\langle w,x,y,z\rangle$.Describe the sets of points in $R^4$ satisfying $||v||=4$.

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Q. 20

What is the set of all position vectors in R2 of magnitude 5 ?

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Q. 21

What is the set of all position vectors in $R^3$ of magnitude $5$?

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