Determine the magnitude of the vector v=(3,4)?(K:1)

Question

BlackTom AI · Accepted Answer

We start by identifying the task: find the magnitude (length) of the vector v = (3, 4).
Option a: 3. This would only be the case if the y-component were 0 and the x-component were 3, or if we were looking at only one coordinate rather than the Euclidean length. It does not account for the second component.
Option b: 4. Similar to option a, 4 would imply focusing on a single coordinate’s magnitude or perhaps misapplying the Pythagorean idea. It ignores the contribution of the other component.
Option c: 7. This value does not satisfy the standard Pythagorean relationship for a two-component vector with components 3 and 4; it’s larger than the sum of squares would allow for these components.
Option d: 5. This matches the Pythagorean calculation for the magnitude: sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. It correctly combines the two perpendicular components to yield the vector’s length.

Determine the magnitude of the vector v=(3,4)?(K:1)

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