MHT CET · Maths · Vector Algebra
ABCD is a quadrilateral with \(\overline{\mathrm{AB}}=\bar{a}, \overline{\mathrm{AD}}=\overline{\mathrm{b}}\) and \(\overline{\mathrm{AC}}=2 \bar{a}+3 \overline{\mathrm{~b}}\). If its area is \(\alpha\) times the area of the parallelogram with \(\mathrm{AB}, \mathrm{AD}\) as adjacent sides, then the value of \(\alpha\) is
- A \(\frac{1}{2}\)
- B \(\frac{5}{2}\)
- C \(\frac{3}{2}\)
- D 2
Answer & Solution
Correct Answer
(B) \(\frac{5}{2}\)
Step-by-step Solution
Detailed explanation
\(\overline{\mathrm{BD}} = \overline{\mathrm{AD}} - \overline{\mathrm{AB}} = \overline{\mathrm{b}} - \bar{a}\) \(\overline{\mathrm{AC}} \times \overline{\mathrm{BD}} = (2 \bar{a}+3 \overline{\mathrm{b}}) \times (\overline{\mathrm{b}} - \bar{a})\)
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