Calculate the cross product u x v for u = <1, 0, 0> and v = <0, 1, 0> in standard basis.
Answer and explanation
Correct answer: B. <0, 0, 1>
- Step 1: Recall the standard unit vector cross product: i x j = k.
- Step 2: Here, u = i = <1, 0, 0> and v = j = <0, 1, 0>.
- Step 3: By right-hand rule and determinant expansion: u x v = k = <0, 0, 1>.
Answer
<0, 0, 1>.
Why not the others: '<0, 0, -1>' reverses the cross product order (j x i = -k); '<1, 1, 0>' adds vectors rather than computing cross product; '<0, 0, 0>' occurs for parallel vectors.
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