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NDA 2022 Maths · Mathematics · Vector Algebra · easy

The dot product of two vectors is a scalar. 2. |vec a×vec b|=|vec a||vec b|cos θ, where θ is the angle between them.

Single correct option

Which of the following statements is/are correct?
1. The dot product of two vectors is a scalar.
2. ∣a⃗×b⃗∣=∣a⃗∣∣b⃗∣cos⁡θ|\vec a\times\vec b|=|\vec a||\vec b|\cos\theta, where θ\theta is the angle between them.
  1. A. 11 only
  2. B. 22 only
  3. C. Both 11 and 22
  4. D. Neither 11 nor 22
Show answer and solution

Answer: (A) 11 only

The dot product is a scalar, so Statement 1 holds. The magnitude of the cross product is ∣a⃗∣∣b⃗∣sin⁡θ|\vec a||\vec b|\sin\theta, not cos⁡θ\cos\theta (that is the dot product), so Statement 2 is false. Only Statement 1.
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Original question written in the NDA 2022 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake