Last updated at May 29, 2018 by Teachoo

Transcript

Ex 10.4, 12 Area of a rectangle having vertices A, B, C and D with position vectors − 𝑖 + 12 𝑗 + 4 𝑘, 𝑖 + 12 𝑗 + 4 𝑘, 𝑖 − 12 𝑗 + 4 𝑘, − 𝑖 − 12 𝑗 + 4 𝑘 respectively is (A) 12 (B) 1 (C) 2 (D) 4 𝑂𝐴 = − 𝑖 + 12 𝑗 + 4 𝑘 = −1 𝑖 + 12 𝑗 + 4 𝑘 𝑂𝐵 = 𝑖 + 12 𝑗 + 4 𝑘 = 1 𝑖 + 12 𝑗 + 4 𝑘 𝑂𝐶 = 𝑖 − 12 𝑗 + 4 𝑘 = 1 𝑖 - 12 𝑗 + 4 𝑘 𝑂𝐷 = − 𝑖 − 12 𝑗 + 4 𝑘 = −1 𝑖 – 12 𝑗 + 4 𝑘 Since rectangle is also a parallelogram Area of rectangle ABCD = 𝐴𝐵× 𝐵𝐶 Now, Magnitude of 𝐴𝐵× 𝐵𝐶 = 02+02+ −22 𝑨𝑩× 𝑩𝑪 = 4 = 2 Therefore, area of rectangle ABCD = 𝐴𝐵× 𝐵𝐶 = 2 Hence, (C) is the correct option

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.