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JEE Main 2023 · Mathematics · Vector Algebra · easy

The projection of vec a=hat i+2hat j+2hat k on vec b=2hat i-hat j+2hat k is

Single correct option

The projection of a⃗=i^+2j^+2k^\vec a=\hat i+2\hat j+2\hat k on b⃗=2i^−j^+2k^\vec b=2\hat i-\hat j+2\hat k is
  1. A. 43\dfrac43
  2. B. 44
  3. C. 49\dfrac{4}{9}
  4. D. 83\dfrac{8}{3}
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Answer: (A) 43\dfrac43

a⃗⋅b⃗=2−2+4=4\vec a\cdot\vec b=2-2+4=4 and ∣b⃗∣=4+1+4=3|\vec b|=\sqrt{4+1+4}=3. The scalar projection is a⃗⋅b⃗∣b⃗∣=43\dfrac{\vec a\cdot\vec b}{|\vec b|}=\dfrac43. Dividing by ∣b⃗∣2|\vec b|^2 instead gives the common wrong value 49\tfrac49.
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Original question written in the JEE Main 2023 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake