TS EAMCET · Maths · Vector Algebra
\(7 \bar{i}-4 \bar{j}+7 \bar{k}, \bar{i}-6 \bar{j}+10 \bar{k},-\bar{i}-3 \bar{j}+4 \bar{k}, 5 \bar{i}-\bar{j}+\bar{k}\) are the position vectors of the points \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}\) respectively. If \(p \bar{i}+q \bar{j}+r \bar{k}\) is the position vector of the point of intersection of the diagonals of the quadrilateral ABCD, then \(p+q+r=\)
- A \(4\)
- B \(5\)
- C \(0\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
\(\vec{p} = \frac{\vec{a} + \vec{c}}{2}\) \(\vec{p} = \frac{(7\bar{i}-4\bar{j}+7\bar{k}) + (-\bar{i}-3\bar{j}+4\bar{k})}{2}\) \(\vec{p} = \frac{6\bar{i}-7\bar{j}+11\bar{k}}{2}\) \(\vec{p} = 3\bar{i} - \frac{7}{2}\bar{j} + \frac{11}{2}\bar{k}\)…
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