JEE Mains · Maths · STD 12 - 10. vector algebra
If \(\mathrm{A}(3,1,-1), \mathrm{B}\left(\frac{5}{3}, \frac{7}{3}, \frac{1}{3}\right), \mathrm{C}(2,2,1)\) and \(\mathrm{D}\left(\frac{10}{3}, \frac{2}{3}, \frac{-1}{3}\right)\) are the vertices of a quadrilateral \(\mathrm{ABCD}\), then its area is
- A \(\frac{4 \sqrt{2}}{3}\)
- B \(\frac{5 \sqrt{2}}{3}\)
- C \(2 \sqrt{2}\)
- D \(\frac{2 \sqrt{2}}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{4 \sqrt{2}}{3}\)
Step-by-step Solution
Detailed explanation
Area \(=\frac{1}{2}|\overline{\mathrm{BD}} \times \overline{\mathrm{AC}}|\) \( \overline{\mathrm{BD}}=\frac{5}{3} \hat{\mathrm{i}}-\frac{5}{3} \hat{\mathrm{j}}-\frac{2}{3} \hat{\mathrm{k}} \) \( \overline{\mathrm{AC}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}-2 \hat{\mathrm{k}}\)
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