AP EAMCET · Maths · Three Dimensional Geometry
Let \(A B C D\) be a parallelogram and \(2 \hat{i}+\hat{j}, 4 \hat{i}+5 \hat{j}+4 \hat{k}\) and \(-\hat{i}-4 \hat{j}-3 \hat{k}\) be the position vectors of the vertices \(A, B\), \(D\) respectively. Then the position vector of one of the point of trisection of the diagonal \(\mathrm{AC}\) is
- A \(\frac{1}{3}(5 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}})\)
- B \(\frac{1}{3}(5 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})\)
- C \(\frac{1}{3}(5 \hat{i}+4 \hat{j}+\hat{k})\)
- D \(\frac{1}{3}(3 \hat{i}+2 \hat{j}+\hat{k})\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{3}(5 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}})\)
Step-by-step Solution
Detailed explanation
Since diagonals of parallelogram bisect each other at mid point. Hence coordinates of \(\mathrm{M}\) \[ \begin{aligned} & =\left(\frac{-1+4}{2}, \frac{-4+5}{2}, \frac{-3+4}{2}\right) \\ & =\left(\frac{3}{2}, \frac{1}{2}, \frac{1}{2}\right) \end{aligned} \] Since \(M\) is also…
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