Find the length of the vector
x=[7
5
−2].

Question

BlackTom AI · Accepted Answer

The problem asks for the length (norm) of the vector x = [7, 5, −2].

First, recall that the Euclidean length of a 3D vector [a, b, c] is sqrt(a^2 + b^2 + c^2).

Compute each square: 7^2 = 49, 5^2 = 25, (−2)^2 = 4.

Add them together: 49 + 25 + 4 = 78.

Take the square root of the sum: sqrt(78).

Thus, the magnitude (length) of the vector x is sqrt(78). This result is consistent with the definition of the vector norm in Euclidean space.

If you were to compare nearby numeric values for intuition: sqrt(64) = 8 and sqrt(81) = 9, so sqrt(78) is between 8 and 9, closer to 9 since 78 is near 81. This helps sanity-check the magnitude relative to the component sizes.

MATH1061/1002/1021 (ND) Early Feedback Task: MATH1061 Canvas Quiz 2

Find the length of the vector x=[7 5 −2].

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