Let u = i + j , v = i - j and w = 2i + 3j + k . If n is a unit vector such that u × n = 0 and v × n = 0 , then |w × n| is equal to: - Mathematics MCQ AIEEE-CBSE-ENG-03 2026 | ExamTest.live

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Let u = \hat{i} + \hat{j}, v = \hat{i} - \hat{j} and w = 2 \hat{i} + 3 \hat{j} + \hat{k} . If \overset{n}{^} is a unit vector such that u \cdot \overset{n}{^} = 0 and v \cdot \overset{n}{^} = 0, then ∣ w \cdot \overset{n}{^} ∣ is equal to:

Solution & Step-by-step Explanation

Since \overset{n}{^} is perpendicular to both u and v, it must be parallel to u \times v . u \times v = \hat{i} 11 \hat{j} 1 - 1 \hat{k} 00 = 0 \hat{i} + 0 \hat{j} - 2 \hat{k} Magnitude is 2. The unit vector \overset{n}{^} is \pm \hat{k} . Now find ∣ w \cdot \overset{n}{^} ∣ : ∣ w \cdot \overset{n}{^} ∣ = ∣ (2 \hat{i} + 3 \hat{j} + \hat{k}) \cdot \hat{k} ∣ = ∣1∣ = 1

Try it yourself before checking the explanation above.

Let u = \hat{i} + \hat{j}, v = \hat{i} - \hat{j} and w = 2 \hat{i} + 3 \hat{j} + \hat{k} . If \overset{n}{^} is a unit vector such that u \cdot \overset{n}{^} = 0 and v \cdot \overset{n}{^} = 0, then ∣ w \cdot \overset{n}{^} ∣ is equal to:

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