Question 10 (OR 1 st question)
Find the area of the parallelogram whose diagonals are represented by the vectors a = 2i – 3j + 4k and b = 2i – j + 2k
We use the Area of Parallelogram formula with Diagonals
Last updated at Oct. 30, 2019 by Teachoo
Question 10 (OR 1 st question)
Find the area of the parallelogram whose diagonals are represented by the vectors a = 2i – 3j + 4k and b = 2i – j + 2k
We use the Area of Parallelogram formula with Diagonals
Transcript
Question 10 (OR 1st question) Find the area of the parallelogram whose diagonals are represented by the vectors ๐ โ = 2๐ ฬ โ 3๐ ฬ + 4๐ ฬ and ๐ โ = 2๐ ฬ โ ๐ ฬ + 2๐ ฬ Area of parallelogram with diagonals Area = 1/2 |(๐_1 ) โร(๐_2 ) โ | Given Diagonals of a parallelogram as ๐ โ = 2๐ ฬ โ 3๐ ฬ + 4๐ ฬ and ๐ โ = 2๐ ฬ โ ๐ ฬ + 2๐ ฬ Area of the parallelogram = 1/2 |๐ โร๐ โ | Finding ๐ โ ร ๐ โ ๐ โ ร ๐ โ = |โ 8(๐ ฬ&๐ ฬ&๐ ฬ@2&โ3&4@2&โ1&2)| = ๐ ฬ ((โ3) ร 2 โ (-1) ร 4) โ ๐ ฬ (2 ร 2 โ 2 ร 4) + ๐ ฬ (2 ร (-1) โ 2 ร (-3)) = ๐ ฬ (-6 + 4) โ ๐ ฬ (4 โ 8) + ๐ ฬ (โ2 + 6) = ๐ ฬ (โ2) - ๐ ฬ (โ4) + ๐ ฬ (4) = โ2๐ ฬ + 4๐ ฬ + 4๐ ฬ So, Magnitude of ๐ โ ร ๐ โ = โ((โ2)2+(4)2+(4)2) |๐ โ" ร " ๐ โ | = โ(4+16+16) |๐ โ" ร " ๐ โ |= โ36 |๐ โ" ร " ๐ โ |= 6 Thus, Area of the parallelogram = 1/2 |๐ โร๐ โ | = 1/2 ร 6 = 3 square units
CBSE Class 12 Sample Paper for 2019 Boards
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Question 4 (Or 1st)
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Question 5
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Question 10 (Or 1st) You are here
Question 10 (Or 2nd)
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CBSE Class 12 Sample Paper for 2019 Boards
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