Compute the magnitude of the cross product |a × b| for a = (1,2,3) and b = (−1,0,1).

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Multiple Choice

Compute the magnitude of the cross product |a × b| for a = (1,2,3) and b = (−1,0,1).

The magnitude of the cross product measures the area of the parallelogram spanned by the two vectors, and you find it by computing a × b and then taking its length. Compute a × b using the determinant: a × b = (2, -4, 2). Then its magnitude is |a × b| = sqrt(2^2 + (-4)^2 + 2^2) = sqrt(4 + 16 + 4) = sqrt(24) = 2√6. So the result is 2√6.

The magnitude of the cross product measures the area of the parallelogram spanned by the two vectors, and you find it by computing a × b and then taking its length.

Compute a × b using the determinant:

a × b = (2, -4, 2).

Then its magnitude is

|a × b| = sqrt(2^2 + (-4)^2 + 2^2) = sqrt(4 + 16 + 4) = sqrt(24) = 2√6.

So the result is 2√6.

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