Given the vectors u = (1, 3, 0) and v = (0, 1, -1), which of the following is the cross product of u with v? Group of answer choices (-3, 1, 2) (-3, 1, 1) (2, 2, 2) 3
Question
Given the vectors u = (1, 3, 0) and v = (0, 1, -1), which of the following is the cross product of u with v? Group of answer choices
(-3, 1, 2)
(-3, 1, 1)
(2, 2, 2)
3
Solution
The cross product of two vectors u = (u1, u2, u3) and v = (v1, v2, v3) is given by the formula:
w = (u2v3 - u3v2, u3v1 - u1v3, u1v2 - u2v1)
So, for u = (1, 3, 0) and v = (0, 1, -1), we have:
w1 = u2v3 - u3v2 = 3*(-1) - 01 = -3 w2 = u3v1 - u1v3 = 00 - 1*(-1) = 1 w3 = u1v2 - u2v1 = 11 - 30 = 1
So, the cross product of u with v is (-3, 1, 1).
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