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AP EAMCET · Maths · Vector Algebra

\(\bar{a}, \bar{b}\) and \(\bar{c}\) are the position vectors of three non-collinear points on a plane. If \(\alpha=\left[\begin{array}{lll}\overline{\mathrm{a}} & \overline{\mathrm{b}} & \overline{\mathrm{c}}\end{array}\right]\) and \(\overline{\mathrm{r}}=\overline{\mathrm{a}} \times \overline{\mathrm{b}}-\overline{\mathrm{c}} \times \overline{\mathrm{b}}-\overline{\mathrm{a}} \times \overline{\mathrm{c}}\), then \(\frac{|\alpha|}{|\overline{\mathrm{r}}|}\) represents

  1. A Ratio of areas of the triangles formed by \(\bar{o}, \bar{a}, \bar{b}\) to \(\bar{o}, \bar{b}, \bar{c}\)
  2. B Ratio of the numerical values of volume of the parallelopiped formed with \(\overline{\mathrm{o}}, \overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) and its height
  3. C Ratio of lengths of the diagonals of the parallelopiped formed with \(\overline{\mathrm{o}}, \overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\)
  4. D Length of the perpendicular from origin to the plane
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Answer & Solution

Correct Answer

(D) Length of the perpendicular from origin to the plane

Step-by-step Solution

Detailed explanation

\overline{\mathrm{r}}=\overline{\mathrm{a}} \times \overline{\mathrm{b}}-\overline{\mathrm{c}} \times \overline{\mathrm{b}}-\overline{\mathrm{a}} \times \overline{\mathrm{c}} = \overline{\mathrm{a}} \times \overline{\mathrm{b}} + \overline{\mathrm{b}} \times…

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