Suppose v = 2i + j - k and w = i + 3k . If u is a unit vector, then the maximum value of the scalar triple product [u v w] is: - Mathematics MCQ Mathematics Mock Test - 5 2026 | ExamTest.live

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Suppose v = 2 \hat{i} + \hat{j} - \hat{k} and w = \hat{i} + 3 \hat{k} . If u is a unit vector, then the maximum value of the scalar triple product [u v w] is:

Solution & Step-by-step Explanation

The scalar triple product is [u v w] = u \cdot (v \times w) .First, calculate v \times w : v \times w = \hat{i} 21 \hat{j} 10 \hat{k} - 1 3 = \hat{i} (3 - 0) - \hat{j} (6 - (- 1)) + \hat{k} (0 - 1) = 3 \hat{i} - 7 \hat{j} - \hat{k} The magnitude ∣ v \times w ∣ = 3^{2} + (- 7)^{2} + (- 1)^{2} = 9 + 49 + 1 = 59 .Since u is a unit vector, [u v w] = ∣ u ∣∣ v \times w ∣ cos θ = 59 cos θ .The maximum value occurs when cos θ = 1, which is 59 .

Try it yourself before checking the explanation above.

Suppose v = 2 \hat{i} + \hat{j} - \hat{k} and w = \hat{i} + 3 \hat{k} . If u is a unit vector, then the maximum value of the scalar triple product [u v w] is:

10 + 6

59

- 1

6

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