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AP EAMCET · Maths · Vector Algebra

\(\vec{c}\) is a vector along the bisector of the internal angle between the vectors \(\vec{a}=4 \hat{i}+7 \hat{j}-4 \hat{k}\) and \(\vec{b}=12 \hat{i}-3 \hat{j}+4 \hat{k}\). If the magnitude of \(\vec{c}\) is \(3 \sqrt{13}\) then \(\vec{c}=\)

  1. A \(5 \hat{i}-8 \hat{j}+2 \sqrt{2} \hat{k}\)
  2. B \(10 \hat{i}+4 \hat{j}-\hat{k}\)
  3. C \(\hat{i}-10 \hat{j}+4 \hat{k}\)
  4. D \(2 \sqrt{2} \hat{i}+5 \hat{j}-8 \hat{k}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(10 \hat{i}+4 \hat{j}-\hat{k}\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { (b) } \vec{a}=4 \hat{i}+7 \hat{j}-4 \hat{k}, \vec{b}=12 \hat{i}-3 \hat{j}+4 \hat{k} \\ & \mathrm{U}_{\vec{a}}=\frac{4 \hat{i}+7 \hat{j}-4 \hat{k}}{9}, \mathrm{U}_{\vec{b}}=\frac{12 \hat{i}-3 \hat{j}+4 \hat{k}}{13} \end{aligned}\) unit vector along…