AP EAMCET · Maths · Vector Algebra
In \(\triangle P Q R,(4 \hat{i}+3 \hat{j}+6 \hat{k}),(2 \hat{i}+2 \hat{j}+3 \hat{k})\) and \((3 \hat{i}+\hat{j}+3 \hat{k})\) are the position vectors of the vertices \(\mathrm{P}, \mathrm{Q}\) and R respectively. Then the position vector of the point of intersection of the angle bisector of P with QR is
- A \(6 \hat{i}+5 \hat{j}+9 \hat{k}\)
- B \(2 \hat{i}-\hat{j}+3 \hat{k}\)
- C \((5 \hat{i}+3 \hat{j}-2 \hat{k})\)
- D \(\frac{5}{2} \hat{i}+\frac{3}{2} \hat{j}+3 \hat{k}\)
Answer & Solution
Correct Answer
(D) \(\frac{5}{2} \hat{i}+\frac{3}{2} \hat{j}+3 \hat{k}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & P R=\sqrt{1+4+9}=\sqrt{14} \\ & P Q=\sqrt{4+1+9}=\sqrt{14} \\ & P R=P Q\end{aligned}\) \(\triangle P Q R\) is isoceles triangle. Let \(A\) be the position vector of point of intersection of angle bisector of angle \(P\) and \(Q R\). \(A\) is mid point of…
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