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Let a = î - k̂, b = xî + ĵ + (1-x)k̂ and c = yî + xĵ + (1+x-y)k̂. Then [a, b, c] depends on

1. only y
2. only x
3. both x and y
4. neither x nor y

Correct answer: neither x nor y

Solution

The scalar triple product [ a, b, c] is determined by the vectors' linear independence and their orientation in space, which in this case does not change with variations in x or y, indicating that the result is independent of both variables.

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