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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Vector Algebra

NDA 2015 · Mathematics · Vector Algebra

If | a + b |=| a - b | , then which one of the following is correct?

If ∣a⃗+b⃗∣=∣a⃗−b⃗∣|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|, then which one of the following is correct?

Options

  1. Aa⃗=λb⃗\vec{a}=\lambda \vec{b} for some scalar λ\lambda
  2. Ba⃗\vec{a} is parallel to b⃗\vec{b}
  3. Ca⃗\vec{a} is perpendicular to b⃗\vec{b}
  4. Da⃗=b⃗=0→\vec{a}=\vec{b}=\overrightarrow{0}

Correct answer

C. a⃗\vec{a} is perpendicular to b⃗\vec{b}

Step-by-step solution

If ∣a⃗+b⃗∣=∣a⃗−b⃗∣|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}| We know that when (a⃗+b⃗)⋅(a⃗−b⃗)=0(\vec{a}+\vec{b}) \cdot(\vec{a}-\vec{b})=0, then a⃗\vec{a} is perpendicular to b→\overrightarrow{\mathrm{b}}. =a⃗⋅a⃗−a⃗⋅b⃗+b⃗⋅a⃗−b⃗⋅b⃗=0a⃗=\vec{a} \cdot \vec{a}-\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{a}-\vec{b} \cdot \vec{b}=0\vec{a} is perpendicular to b⃗∴\vec{b}\therefore \quad Option (C) is correct.
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