8. Vectors

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

<IMAGE>

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

<IMAGE>

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

<IMAGE>

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

<IMAGE>

Find the angle between the vectors. Round to the nearest tenth of a degree. If the vectors are orthogonal, say so.

〈5, -3〉, 〈3, 5〉

Solve each problem. See Examples 5 and 6.

Distance and Direction of a Motorboat A motorboat sets out in the direction N 80° 00′ E. The speed of the boat in still water is 20.0 mph. If the current is flowing directly south, and the actual direction of the motorboat is due east, find the speed of the current and the actual speed of the motorboat.

<IMAGE>