Let a = i - k , b = xi + j + (1 - x)k and c = yi + xj + (1 + x - y)k . Then [a b c] depends on: - Mathematics MCQ AIEEE 2026 | ExamTest.live

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Let a = \hat{i} - \hat{k}, b = x \hat{i} + \hat{j} + (1 - x) \hat{k} and c = y \hat{i} + x \hat{j} + (1 + x - y) \hat{k} . Then [a b c] depends on:

Solution & Step-by-step Explanation

Calculate the scalar triple product: [a b c] = 1 x y 01 x - 1 1 - x 1 + x - y Expand along the first row: = 1 (1 (1 + x - y) - x (1 - x)) - 0 - 1 (x^{2} - y) = (1 + x - y - x + x^{2}) - (x^{2} - y) = 1 + x^{2} - y - x^{2} + y = 1 The result is 1, which is independent of both x and y .

Try it yourself before checking the explanation above.

Let a = \hat{i} - \hat{k}, b = x \hat{i} + \hat{j} + (1 - x) \hat{k} and c = y \hat{i} + x \hat{j} + (1 + x - y) \hat{k} . Then [a b c] depends on:

only y

only x

both x and y

neither x nor y

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