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If \(\rm |\vec{a}|=3,|\vec{b}|=4\), then a value of λ for which \(\rm \vec{a}+\lambda \vec{b}\) is perpendicular to \(\rm \vec{a}-\lambda \vec{b} \) is :

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  1. \( \frac{9}{16}\)
  2. \( \frac{3}{4}\)
  3. \( \frac{3}{2}\)
  4. \( \frac{4}{3}\)

Answer (Detailed Solution Below)

Option 2 : \( \frac{3}{4}\)
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Detailed Solution

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Calculation 

a + λb is perpendicular to a - λb

∴ (a + λb) ⋅ (a - λb) = 0

|a|2 - λ × (a ⋅ b) + λ × (b ⋅ a) - λ2 × |b|2 = 0

⇒ |a|2 - λ2 × |b|2 = 0

λ = ± \(\frac{|a|}{|b|}\) = ±\(\frac{3}{4}\)

Hence option 2 is correct

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