Step by step Answer:
The answer to the magnitude and direction of a vector would remind you of the Pythagoras theorem.
The magnitude or vector length is the vector sum of it's two components, in the case of <-5, -7>, the components are -5 and -7.
The vector sum (because -5 goes horizontally, and -7 goes vertically) is therefore the hypotenuse of a right triangle with legs 5 and 7, i.e.
magnitude = sqrt ( 5^2 + 7^2) = sqrt (25+49) = sqrt(74) = 8.602
[ note that the question requires the integer before taking square-root, 74 ]
The angle is a little more complex, because with the two components -5, -7, we have to determine the quadrant the angle falls on, based on the sign of each component.
Recall:
<+,+> => Q1
<-,+> => Q2
<-,-> => Q3
<+,-> => Q4
So we know that the angle falls in the third quadrant, since both components are negative.
The angle with the x-axis is obtained by inverse tangent of (y/x), in this case, arctan(-7/(-5) = arctan(7/5)=arctan(1.4)= 54.462 degrees.
Add 180 degrees to get 234.462 degrees from the positive x-axis.
Rounding to the nearest degree gives 234 degrees (from the positive x-axis).
See also image attached.