If A ( 3 , 1 , − 1 ) , B ( 3 5 , 3 7 , 3 1 ) , C ( 2 , 2 , 1 ) and D ( 3 10 , 3 2 , 3 − 1 ) are the vertices of a quadrilateral A BC D , then its area is

Area = 2 1 ∣ BD × AC ∣ BD = 3 5 i ^ − 3 5 j ^ − 3 2 k ^ AC = i ^ − j ^ − 2 k ^

Mathematics - Straight Lines Question with Solution | TestHub

MathematicsStraight LinesGeneral (Standard forms)Medium2 minPYQ_2024

MathematicsMediumsingle choice

If $A (3, 1, - 1), B (\frac{5}{3}, \frac{7}{3}, \frac{1}{3}), C (2, 2, 1)$ and $D (\frac{10}{3}, \frac{2}{3}, \frac{- 1}{3})$ are the vertices of a quadrilateral $A BC D$ , then its area is

Options:

Answer:

Solution:

Area $= \frac{1}{2} ∣ \overline{BD} \times \overline{AC} ∣$ $\overline{BD} = \frac{5}{3} \hat{i} - \frac{5}{3} \hat{j} - \frac{2}{3} \hat{k} \overline{AC} = \hat{i} - \hat{j} - 2 \hat{k}$

Stream:JEESubject:MathematicsTopic:Straight LinesSubtopic:General (Standard forms)

⏱ 2mℹ️ Source: PYQ_2024

Doubts & Discussion

Loading discussions...