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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Vector Algebra

NDA 2012 · Mathematics · Vector Algebra

The vectors a ×( b × a ) is coplanar with :

The vectors a⃗×(b⃗×a⃗)\vec{a} \times(\vec{b} \times \vec{a}) is coplanar with :

Options

  1. Aa⃗\vec{a} only
  2. Bb⃗\vec{b} only
  3. CBoth a⃗\vec{a} and b⃗\vec{b}
  4. DNeither a⃗\vec{a} nor b⃗\vec{b}

Correct answer

C. Both a⃗\vec{a} and b⃗\vec{b}

Step-by-step solution

aˉ×(bˉ×aˉ)⇒(aˉ⋅aˉ)bˉ−(aˉ⋅bˉ)aˉ⇒λbˉ−μaˉ= coplanar with aˉbˉ\begin{aligned} & \bar{a} \times(\bar{b} \times \bar{a}) \\ & \Rightarrow(\bar{a} \cdot \bar{a}) \bar{b}-(\bar{a} \cdot \bar{b}) \bar{a} \\ & \Rightarrow \lambda \bar{b}-\mu \bar{a}=\text{ coplanar with } \bar{a} & \bar{b}\end{aligned}
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