Please help solve this question and explain why, thanks. Vector A is 3.00 units

Question

Please help solve this question and explain why, thanks.

Vector A is 3.00 units in magnitude and points along the positive x-axis. Vector B is 4.00 units in magnitude and points along the negative y-axis. Let C = A + B and D = A – B. Which of the following is true

A. The magnitude of C < The magnitude of D

B. The magnitude of C > The magnitude of D

C. The magnitude of (C – D) = The magnitude of (C + D)

D. The magnitude of (C – D) > The magnitude of (C + D)

E. The magnitude of (C – D) < The magnitude of (C + D)

Explanation / Answer

a = 3i

b = -4j

c = a+b = 3i-4j

magnitude of c = sqrt(3^2+4^2) = 5 units

d = a-b = 3i+4j

magnitude of d = 5 units

c-d = 2b = -8j

magnitude = 8 units

c+d = 2a = 6i

magnitude = 6 units

The magnitude of (C – D) > The magnitude of (C + D)

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