TS EAMCET · Maths · Vector Algebra
Let \(\mathrm{ABC}\) be a triangle and \(\bar{a}, \bar{b}, \bar{c}\) be the position vectors of \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) respectively, Let \(\mathrm{D}\) divide \(\mathrm{BC}\) in the ratio \(3: 1\) internally and \(\mathrm{E}\) divide \(\mathrm{AD}\) in the ratio \(4: 1\) internally. Let \(\mathrm{BE}\) meet \(\mathrm{AC}\) in \(\mathrm{F}\). If \(\mathrm{E}\) divides \(\mathrm{BF}\) in the ratio \(3: 2\) internally then the position vector of \(\mathrm{F}\) is
- A \(\frac{\bar{a}+\bar{b}+\bar{c}}{3}\)
- B \(\frac{\bar{a}-2 \bar{b}+3 \bar{c}}{2}\)
- C \(\frac{\bar{a}+2 \bar{b}+3 \bar{c}}{2}\)
- D \(\frac{\bar{a}-\bar{b}+3 \bar{c}}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{\bar{a}-\bar{b}+3 \bar{c}}{3}\)
Step-by-step Solution
Detailed explanation
Here we are given that \(\overline{\mathrm{OA}}=\overrightarrow{\mathrm{a}}, \overline{\mathrm{OB}}=\overrightarrow{\mathrm{b}}, \overline{\mathrm{OC}}=\overline{\mathrm{c}}\) Now P.V of D i.e…
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