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NDA 2024 Maths · Mathematics · Vector Algebra · medium

The component (scalar projection) of 3hat i+4hat j along hat i+hat j is

Single correct option

The component (scalar projection) of 3i^+4j^3\hat i+4\hat j along i^+j^\hat i+\hat j is
  1. A. 77
  2. B. 72\frac{7}{\sqrt2}
  3. C. 727\sqrt2
  4. D. 12\frac{1}{\sqrt2}
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Answer: (B) 72\frac{7}{\sqrt2}

Scalar projection =a⃗⋅b⃗∣b⃗∣=3+42=72=\frac{\vec a\cdot\vec b}{|\vec b|}=\frac{3+4}{\sqrt2}=\frac{7}{\sqrt2}. Trap: 7 forgets to divide by ∣b⃗∣|\vec b|, and 727\sqrt2 multiplies instead of dividing. Using a unit vector first, i^+j^2\frac{\hat i+\hat j}{\sqrt2}, makes the dot product directly give the component.
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Original question written in the NDA 2024 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