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NDA 2020 Maths · Mathematics · Vector Algebra · medium

The scalar projection of hat i+2hat k on 2hat i+3hat j+6hat k is

Single correct option

The scalar projection of i^+2k^\hat i+2\hat k on 2i^+3j^+6k^2\hat i+3\hat j+6\hat k is
  1. A. 1414
  2. B. 27\dfrac27
  3. C. 67\dfrac67
  4. D. 22
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Answer: (D) 22

The dot product is 1⋅2+0⋅3+2⋅6=141\cdot2+0\cdot3+2\cdot6=14 and ∣2i^+3j^+6k^∣=4+9+36=7|2\hat i+3\hat j+6\hat k|=\sqrt{4+9+36}=7. The scalar projection of a⃗\vec a on b⃗\vec b is a⃗⋅b⃗∣b⃗∣=147=2\dfrac{\vec a\cdot\vec b}{|\vec b|}=\dfrac{14}{7}=2. The value 1414 is the dot product alone, and 27\dfrac27 divides by ∣b⃗∣2=49|\vec b|^2=49, which gives the multiplier of b⃗\vec b in the vector projection instead.
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