Question

Write each of the following vectors in the polar form ⟨r,θ⟩ where rr is the vector's magnitude (in miles) and θ is the vector's angle (in degrees) swept counter-clockwise from the due east direction.Your answers should be in the form "< #, # >" and you do not need to enter a degree symbol.12 miles in the direction 45° north of east.⟨r,θ⟩=1.59 miles in the direction 10° west of south.⟨r,θ⟩=5.7 miles in the direction opposite of 35° south of east.⟨r,θ⟩=

Answer 1

To write the vectors in polar form, we find the magnitude and direction of each vector. The first vector is ⟨12, 45°⟩, the second vector is ⟨1.59, -10°⟩, and the third vector is ⟨5.7, 35°⟩.

Step-by-step explanation:

To write each vector in polar form, we need to find the magnitude and direction of the vector.

For the first vector, 12 miles in the direction 45° north of east, the magnitude is 12 miles and the angle is 45° north of east, which is the same as 45° east of north. The polar form is ⟨12, 45°⟩.

For the second vector, 1.59 miles in the direction 10° west of south, the magnitude is 1.59 miles and the angle is 10° west of south. The polar form is ⟨1.59, -10°⟩.

For the third vector, 5.7 miles in the direction opposite of 35° south of east, the magnitude is 5.7 miles and the angle is opposite of 35° south of east, which is the same as 35° north of west. The polar form is ⟨5.7, 35°⟩.

Answer 2

We are asked to write each of the following vectors in the polar form ⟨r,θ⟩

Where r is the vector's magnitude (in miles) and θ is the vector's angle (in degrees) swept .

1) 12 miles in the direction 45° north of east:

Let us draw a figure to better understand the problem

As you can see, the magnitude is 12 and the angle is 45° measured counter-clockwise from the due east direction.

`(r,\theta)=(12,45)_{}`

2) 1.59 miles in the direction 10° west of south:

Let us draw a figure to better understand the problem

As you can see, the magnitude is 1.59 and the angle is 190° measured counter-clockwise from the due east direction.

`(r,\theta)=(1.59,190)_{}`

3) 5.7 miles in the direction opposite of 35° south of east:

Let us draw a figure to better understand the problem

Please note that opposite of 35° south of east is west of north.

As you can see, the magnitude is 5.7 and the angle is 145° measured counter-clockwise from the due east direction.

`(r,\theta)=(5.7,145)_{}`