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NDA 2023 Maths · Mathematics · Vector Algebra · easy

If vec a and vec b are perpendicular vectors with |vec a|=3 and |vec b|=4, then |vec a+vec b| is

Single correct option

If a⃗\vec a and b⃗\vec b are perpendicular vectors with ∣a⃗∣=3|\vec a|=3 and ∣b⃗∣=4|\vec b|=4, then ∣a⃗+b⃗∣|\vec a+\vec b| is
  1. A. 77
  2. B. 7\sqrt7
  3. C. 11
  4. D. 55
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Answer: (D) 55

Since a⃗⋅b⃗=0\vec a\cdot\vec b=0, ∣a⃗+b⃗∣2=∣a⃗∣2+∣b⃗∣2=25|\vec a+\vec b|^2=|\vec a|^2+|\vec b|^2=25, so the magnitude is 55. The value 77 is correct only if the vectors are parallel in the same direction.
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