Avector points into the third quadrant, and its x and y components are both negative. if its magnitude is equal to two times the magnitude of its x component, what is the angle between the vector and the positive x axis?

Explanation:

The vector lies in the 3rd quadrant, which means that both its x and y components are negative.

Let's analyze the magnitude now. We know that the magnitude of the vector (let's call it v) is 2 times the magnitude of the x-component:

we know that the magnitude of the x-component is given by

where here is measured as angle below the negative x-direction, since we are in the 3rd quadrant. Substituting into the previous equation,

But this is the angle between the vector and the negative x axis: therefore, the angle between the vector and the positive x axis is

i think the answer would be b

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles