JEE Mains · Maths · STD 12 - 10. vector algebra
Let the position vectors of the vertices \(A, B\) and \(C\) of a triangle be \(2 \hat{i}+2 \hat{j}+\hat{k}, \quad \hat{i}+2 \hat{j}+2 \hat{k}\) and \(2 \hat{i}+\hat{j}+2 \hat{k}\) respectively. Let \(l_1, l_2\) and \(l_3\) be the lengths of perpendiculars drawn from the ortho center of the triangle on the sides \(\mathrm{AB}, \mathrm{BC}\) and \(\mathrm{CA}\) respectively, then \(l_1^2+l_2^2+l_3^2\) equals :
- A \(\frac{1}{5}\)
- B \(\frac{1}{2}\)
- C \(\frac{1}{4}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\triangle \mathrm{ABC}\) is equilateral Orthocentre and centroid will be same \(\mathrm{G}\left(\frac{5}{3}, \frac{5}{3}, \frac{5}{3}\right)\) Mid-point of \( \mathrm{AB} \text { is } \mathrm{D}\left(\frac{3}{2}, 2, \frac{3}{2}\right) \)…
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