Find all points at which |r| is a maximum.
A) (1, 0)
B) (0, 8), (8, 0)
C) (8, 0), (0, 8), (-8, 0), (0, -8)
D) (1, 1), (-1, 1)

Question

Find all points at which |r| is a maximum. 
A) (1, 0) 
B) (0, 8), (8, 0) 
C) (8, 0), (0, 8), (-8, 0), (0, -8) 
D) (1, 1), (-1, 1)

Quizplus · Accepted Answer

If we consider the magnitude of a vector r = (x, y), then we have:

|r| = sqrt(x^2 + y^2)

To find the points at which |r| is a maximum, we need to look for the points where the distance from the origin is greatest. These points lie on the circle centered at the origin with radius equal to the maximum value of |r|.

From the answers provided, only choice C gives us a set of points lying on a circle centered at the origin. These points are (8, 0), (0, 8), (-8, 0), and (0, -8), which form a square with sides of length 16. Therefore, the maximum value of |r| is 16, and the points where this maximum value is attained are the points on this square.

Therefore, choice C is the correct answer.

Find All Points at Which |R| Is a Maximum