AP EAMCET · Maths · Three Dimensional Geometry
In a right angled triangle, if the position vector of the vertex having the right angle is \(-3 \mathrm{i}+5 \mathrm{j}+2 \mathrm{k}\) and the position vector of the midpoint of its hypotenuse is \(6 \mathrm{i}+2 \mathrm{j}+5 \mathrm{k}\), then the position vector of its centroid is
- A \(3 i+3 j+4 k\)
- B \(3 \mathrm{i}+3 \mathrm{j}+3 \mathrm{k}\)
- C \(\frac{3 \mathrm{i}+7 \mathrm{j}+7 \mathrm{k}}{2}\)
- D \(4 \mathrm{j}+3 \mathrm{k}\)
Answer & Solution
Correct Answer
(A) \(3 i+3 j+4 k\)
Step-by-step Solution
Detailed explanation
\( \vec{G} = \frac{\vec{A} + \vec{B} + \vec{C}}{3} \) \( \vec{M} = \frac{\vec{B} + \vec{C}}{2} \implies \vec{B} + \vec{C} = 2\vec{M} \) \( \vec{G} = \frac{\vec{A} + 2\vec{M}}{3} \)…
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