Find the area of the parallelogram whose one side and a diagonal are represented by conitial vectors i ฬ - j ฬ + k ฬ and 4i ฬ + 5k ฬ
Last updated at Oct. 27, 2020 by Teachoo
Transcript
Question 26 Find the area of the parallelogram whose one side and a diagonal are represented by conitial vectors ๐ ฬ โ ๐ ฬ + ๐ ฬ and 4๐ ฬ + 5๐ ฬ Let ABCD be the parallelogram Where ๐ โ = ๐ ฬ โ ๐ ฬ + ๐ ฬ And Diagonal ๐ โ = 4๐ ฬ + 5๐ ฬ Now, ๐ โ + ๐ โ = ๐ โ ๐ โ = ๐ โ โ ๐ โ ๐ โ = (4๐ ฬ + 5๐ ฬ ) โ (๐ ฬ โ ๐ ฬ + ๐ ฬ ) ๐ โ = 3๐ ฬ + ๐ ฬ + 4๐ ฬ Now, Area of parallelogram ABCD = |๐ โ" ร " ๐ โ | ๐ โ ร ๐ โ = |โ 8(๐ ฬ&๐ ฬ&๐ ฬ@1&โ1&1@3&1&4)| = ๐ ฬ (โ1 ร 4 โ 1 ร 1) โ ๐ ฬ (1 ร 4 โ 3 ร 1) + ๐ ฬ (1 ร 1 โ 3 ร โ1) = ๐ ฬ (โ4 โ 1) โ ๐ ฬ (4 โ 3) + ๐ ฬ (1 + 3) = โ5๐ ฬ โ ๐ ฬ + 4๐ ฬ Now, Area of Parallelogram ABCD = |(๐จ๐ฉ) โ ร (๐ฉ๐ช) โ | = โ((โ5)2+(โ1)2+42) = โ(25+1+16) = โ๐๐ square units
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CBSE Class 12 Sample Paper for 2021 Boards
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