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NDA 2017 Maths · Mathematics · Vector Algebra · medium

The component of vec a=2hat i+3hat j-hat k along vec b=hat i-2hat j+2hat k is

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The component of a⃗=2i^+3j^−k^\vec a=2\hat i+3\hat j-\hat k along b⃗=i^−2j^+2k^\vec b=\hat i-2\hat j+2\hat k is
  1. A. 22
  2. B. −6-6
  3. C. −23-\frac23
  4. D. −2-2
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Answer: (D) −2-2

a⃗⋅b⃗=2−6−2=−6\vec a\cdot\vec b=2-6-2=-6 and ∣b⃗∣=3|\vec b|=3, so the scalar component is −63=−2\frac{-6}{3}=-2. The value −6-6 is the dot product, 22 drops the sign, and −23-\frac23 divides by ∣a⃗∣=14|\vec a|=\sqrt{14}-type wrongly or by 99.
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Original question written in the NDA 2017 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