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Chapter 1: Q27P (page 40)

A star is located at<6脳1010,8脳1010,6脳1010>m. A planet is located at<-4脳1010,-9脳1010,6脳1010>m. (a) What is the vector pointing from the star to the planet? (b) What is the vector pointing from the planet to the star?

Short Answer

Expert verified

(a) The vector pointing from star to the planet isr鈫�Ps=-10脳1010,-17脳1010,0m.

(b) The vector pointing from planet to the star isr鈫�Ps=-10脳1010,17脳1010,0m.

Step by step solution

01

Identification of given data

Star r鈫�s=6脳1010,8脳1010,6脳1010m

Planet r鈫�P=-4脳1010,-9脳1010,6脳1010m

02

Calculating vector pointing from star to planet

(a) Here the tail of the vector will be on the star, and the head of it is on the planet, and the position vector between these two points could be found by subtracting the position of the tail from the position of the head.

r鈫�PS=-4脳1010,-9脳1010,6脳1010-6脳1010,8脳1010,6脳1010r鈫�PS=-10脳1010,-17脳1010,0

Thus, the required vector is r鈫�PS=-10脳1010,-17脳1010,0m.

03

Calculating vector pointing from planet to star

(b) The vector pointing from the planet (position of the tail) to the star (position of the head) is the result of subtracting the position of the planet from the position of the star (or simply it is the negative of the position vector from the star to the planet).

r鈫�PS=6脳1010,8脳1010,6脳1010--4脳1010,-9脳1010,6脳1010r鈫�PS=-10脳1010,-17脳1010,0m=-r鈫�SP

Therefore, the required vector is r鈫�PS=-10脳1010,-17脳1010,0mm.

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