Question

Let u = (6, -7), v = (5,4), and w = (8,5). Which has the greater magnitude, u - v or w-u?

Choose the correct answer below.
A. u-v
B. w-u

Answer 1

Option B). After performing vector subtraction for u - v and w - u, the magnitudes are calculated to be the square root of 122 and the square root of 148, respectively. Since the square root of 148 is greater, the vector with the greater magnitude is w - u.

Step-by-step explanation:

First, we need to find the vectors u - v and w - u. To do this, we perform vector subtraction component-wise. For u - v:

• (6, -7) - (5, 4) = (6 - 5, -7 - 4) = (1, -11)

And for w - u:

• (8, 5) - (6, -7) = (8 - 6, 5 - (-7)) = (2, 12)

Next, we calculate the magnitudes of these resulting vectors using the formula for the magnitude of a vector which is the square root of the sum of the squares of its components:

• |u - v| = √(1^2 + (-11)^2) = √(1 + 121) = √122
• |w - u| = √(2^2 + 12^2) = √(4 + 144) = √148

Comparing the magnitudes, √148 is greater than √122, so w - u has the greater magnitude than u - v. Therefore, the correct answer is B. w - u.