AP EAMCET · Maths · Vector Algebra
If \(7 \hat{i}-4 \hat{j}+5 \hat{k}\) is the position vector of the vertex \(A\) of a tetrahedron \(A B C D\) and \(-\hat{i}+4 \hat{j}-3 \hat{k}\) is the position vector of the centroid of the triangle \(\mathrm{BCD}\), then the position vector of the centroid of the tetrahedron \(A B C D\) is
- A \(-\hat{i}+4 \hat{j}-3 \hat{k}\)
- B \(-\frac{1}{2} \hat{i}+4 \hat{j}-3 \hat{k}\)
- C \(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}}\)
- D \(-\hat{i}-2 \hat{j}+\hat{k}\)
Answer & Solution
Correct Answer
(C) \(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} \begin{aligned} \bar{A} & =7 \hat{i}-4 \hat{j}+5 \hat{k} \\ \bar{C}_{B C D} & =\frac{\bar{B}+\bar{C}+\bar{D}}{3}=-\hat{i}+4 \hat{j}-3 \hat{k}\end{aligned} \\ & \text { Centroid of tetrahedron } A B C D \\ & \begin{aligned} \bar{C}_{A B C D} &…
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