If A(1,−1,2),B(5,7,−6),C(3,4,−10) and D(−1,−4,−2) are the vertices of a quadrilateral ABCD, then its area is
(A)2429
(B)487
(C)247
(D)1229✓ Correct
Answer: (D)
Solution
For a quadrilateral ABCD the area is 21∣AC×BD∣. AC=(2,5,−12), BD=(−6,−11,4). AC×BD=(5⋅4−(−12)(−11),(−12)(−6)−2⋅4,2(−11)−5(−6))=(−112,64,8). ∣AC×BD∣=8142+82+12=8261=8⋅329=2429. Area =21(2429)=1229.
JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Single correct option