What Is The Area Of Rectangle Abcd

What Is The Area Of Rectangle Abcd – Ex 10.4, 12 Area of ​​a rectangle with position vectors A, B, C & D at vertices is −𝑖 ̂ + 1/2 𝑗 ̂ + 4𝑘 ̂, 𝑖 ̂ + 1/2 𝑗 ̂ ̂ ̑ 2 ̂ 4𝑘 ̂, − 𝑖 ̂ ̂ – 1/2 𝑗 ̂ + 4𝑘 ̂ respectively (A) 1/2 (B) 1 (C) 2 (D) 4 (𝑂𝐴) 2 𝑗 = ̘1 + 4 4𝑘 ̂ (𝑂𝐶) ⃗ = 𝑖 ̂ − 1/2 𝑗 ̂ + 4𝑘 ̂ = 1🝑 ̂ = −1𝑖 ̂ – 1/2 𝑗 ̝ ) ⃗×(𝐵𝐶 ) ⃗ | (𝑩𝑨) ⃗ = (𝑶𝑩) ⃗ − (𝑶𝑨) ⃗ = (“1″ 𝑖 ̂” + ” 1/2 ” ” 𝑗 ̂” + 4″ 𝑘 ̂ ▒” +2 “̘” 𝑑 ̂” ̂ ) = (“1−(−1)” 𝑖 ̂” +” (1/2−1/2) 𝑗 ̂” + (4 − 4)” ) 𝑘 ̂ = 2𝑖 ̂ + 0𝑗 ̂ + 0𝑘 ̂ (𝑩𝑪 ) ⃗ = (𝑶𝑪) ⃗ − (𝑶𝑩) ⃗ = (“1” 𝑖 ̂”𝑖 ̂ ) – (“1″ 𝑖 ̂” + “1/2 “” 𝑗) ̂” 𝑗 ̂” +4″ (” (1− 1)” 𝑖 ̂” +” (−1/2−1/2) 𝑗 ̂” + ( 4 − 4)” ) 𝑘 ̂ = 0𝑖 ̂ – 1𝑗 ̂ + 0𝑘 ̂ |(𝑨𝑩) ❑ ×( 𝑩𝑪) ⃗ | = |■8(𝑖 ̂&𝑗 ̂&𝑘 ̂@2&0&0@0&−1&0)| = 𝑖 ̂ (0 × 0 − (−1) × 0) − 𝑗 ̂ (2 × 0 − 0 × 0) + 𝑘 ̂ (2 × −1 − 0 × 0 ) = 𝑖 − − ̂ (0 − 0) + 𝑘 ̂ (−2 − 0) = 0𝒊 ̂ − 0𝒋 ̂ − 2𝒌 ̂ Now, (𝐴𝐵) ⃗x 2) |(𝑨𝑩) ⃗×(𝑩𝑪) ) . = √4 = 2 Thus, area of ​​rectangle ABCD = |(𝐴𝐵) ⃗×(𝐵𝐶) ⃗ | = 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.

What Is The Area Of Rectangle Abcd

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Solved: The Area Of The Rectangle Is 100 Square Units. Determine The Area, In Square Units, Of Rectangle Abcd. Enter The Area Of Rectangle Abcd

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