# What Is The Area Of Rectangle Abcd

What Is The Area Of Rectangle Abcd β Ex 10.4, 12 Area of ββa rectangle with position vectors A, B, C & D at vertices is βπ Μ + 1/2 π Μ + 4π Μ, π Μ + 1/2 π Μ Μ Μ 2 Μ 4π Μ, β π Μ Μ β 1/2 π Μ + 4π Μ respectively (A) 1/2 (B) 1 (C) 2 (D) 4 (ππ΄) 2 π = Μ1 + 4 4π Μ (ππΆ) β = π Μ β 1/2 π Μ + 4π Μ = 1π Μ = β1π Μ β 1/2 π Μ ) βΓ(π΅πΆ ) β | (π©π¨) β = (πΆπ©) β β (πΆπ¨) β = (β1β³ π Μβ + β 1/2 β β π Μβ + 4β³ π Μ ββ +2 βΜβ π Μβ Μ ) = (β1β(β1)β π Μβ +β (1/2β1/2) π Μβ + (4 β 4)β ) π Μ = 2π Μ + 0π Μ + 0π Μ (π©πͺ ) β = (πΆπͺ) β β (πΆπ©) β = (β1β π Μβπ Μ ) β (β1β³ π Μβ + β1/2 ββ π) Μβ π Μβ +4β³ (β (1β 1)β π Μβ +β (β1/2β1/2) π Μβ + ( 4 β 4)β ) π Μ = 0π Μ β 1π Μ + 0π Μ |(π¨π©) β Γ( π©πͺ) β | = |β 8(π Μ&π Μ&π Μ@2&0&0@0&β1&0)| = π Μ (0 Γ 0 β (β1) Γ 0) β π Μ (2 Γ 0 β 0 Γ 0) + π Μ (2 Γ β1 β 0 Γ 0 ) = π β β Μ (0 β 0) + π Μ (β2 β 0) = 0π Μ β 0π Μ β 2π Μ Now, (π΄π΅) βx 2) |(π¨π©) βΓ(π©πͺ) ) . = β4 = 2 Thus, area of ββrectangle ABCD = |(π΄π΅) βΓ(π΅πΆ) β | = 2 Therefore (C) is the correct option

Davneet Singh completed his B.Tech from the Indian Institute of Technology, Kanpur. He has been teaching for the past 13 years. He teaches courses in Mathematics, Science, Social Science, Physics, Chemistry and Computer Science.