AP EAMCET · Maths · Vector Algebra
The vertices of a triangle are at \(-\hat{i}+3 \hat{j}\) and \(2 \hat{i}+5 \hat{j}\) and its orthocenter is at \(\bar{i}+2 \bar{j}\). If the position vector of the third vertex is \(a \hat{i}+b \hat{j}\), then \((a, b)=\)
- A \(\left(\frac{5}{7}, \frac{5}{7}\right)\)
- B \(\left(\frac{5}{7}, \frac{17}{7}\right)\)
- C \(\left(\frac{-5}{7}, \frac{17}{7}\right)\)
- D \(\left(\frac{5}{7}, \frac{-17}{7}\right)\)
Answer & Solution
Correct Answer
(B) \(\left(\frac{5}{7}, \frac{17}{7}\right)\)
Step-by-step Solution
Detailed explanation
Let \(A=(-1,3), B=(2,5), C=(a, b), H=(1,2)\). \(\begin{aligned} & A E \perp B C \\ & M_{A E} \times M_{B C}=-1\end{aligned}\) \(\Rightarrow \quad\left(\frac{3-2}{-1-1}\right)\left(\frac{5-b}{2-a}\right)=-1\) \(\Rightarrow \quad 2 a-b=-1\) ...(i) Again…
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