TS EAMCET · Maths · Three Dimensional Geometry
Let \(\vec{a}, \vec{b}, \vec{c}\) be three non-coplanar vectors and \(L\) be the line passing through the points \(\vec{a}-\vec{b}+\vec{c}\) and \(\vec{b}-\vec{c}\). If \(\pi\) is a planepassing through the points \(2 \overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}, 2 \overrightarrow{\mathrm{b}}-\overrightarrow{\mathrm{c}}\) and \(2 \overrightarrow{\mathrm{c}}-\overrightarrow{\mathrm{a}}\), then the point of intersection of \(L\) and \(\pi\) is
- A \(\vec{a}-\vec{b}\)
- B \(\vec{b}+\vec{c}\)
- C \(\bar{c}-\bar{a}\)
- D \(\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}\)
Answer & Solution
Correct Answer
(D) \(\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}\)
Step-by-step Solution
Detailed explanation
Equation of line passing through 2 points \[ \vec{r}=(\vec{a}-\vec{b}+\vec{c})+\lambda(-\vec{a}+2 \vec{b}-2 \vec{c}) \] Equation of plane passing through…
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