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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Vector Algebra

NDA 2013 · Mathematics · Vector Algebra

If a =2 i +2 j +3 k , b =- i +2 j + k and c =3 i + j are three...

If a⃗=2i^+2j^+3k^,b⃗=−i^+2j^+k^\vec{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=-\hat{i}+2 \hat{j}+\hat{k} and c⃗=3i^+j^\vec{c}=3 \hat{i}+\hat{j} are three vectors such that a⃗+tb⃗\vec{a}+t \vec{b} is perpendicular to c⃗\vec{c}, then what is tt equal to?

Options

  1. A8
  2. B6
  3. C4
  4. D2

Correct answer

A. 8

Step-by-step solution

a⃗+tb⃗=(2i^+2j^+3k^)+t(−i^+2j^+k^)=(2−t)i^+(2+2t)j^+(3+t)k^\begin{aligned} \vec{a}+t \vec{b} & =(2 \hat{i}+2 \hat{j}+3 \hat{k})+t(-\hat{i}+2 \hat{j}+\hat{k}) \\ & =(2-t) \hat{i}+(2+2 t) \hat{j}+(3+t) \hat{k} \end{aligned} According to the question, (a⃗+tb⃗)⋅c⃗=0(2−t)⋅3+(2+2t)⋅1=08−t=0⇒t=8(\vec{a}+t \vec{b}) \cdot \vec{c}=0(2-t) \cdot 3+(2+2 t) \cdot 1=08-t=0 \Rightarrow t=8
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