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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

Find area of parallelogram by vectors a = 2i – 3j  + 4k and b = 2i - j

Question 10 (Or 1st) - CBSE Class 12 Sample Paper for 2019 Boards - Part 2
Question 10 (Or 1st) - CBSE Class 12 Sample Paper for 2019 Boards - Part 3

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Transcript

Question 10 (OR 1st question) Find the area of the parallelogram whose diagonals are represented by the vectors š‘Ž āƒ— = 2š‘– Ģ‚ ā€“ 3š‘— Ģ‚ + 4š‘˜ Ģ‚ and š‘ āƒ— = 2š‘– Ģ‚ ā€“ š‘— Ģ‚ + 2š‘˜ Ģ‚ Area of parallelogram with diagonals Area = 1/2 |(š‘‘_1 ) āƒ—Ć—(š‘‘_2 ) āƒ— | Given Diagonals of a parallelogram as š‘Ž āƒ— = 2š‘– Ģ‚ ā€“ 3š‘— Ģ‚ + 4š‘˜ Ģ‚ and š‘ āƒ— = 2š‘– Ģ‚ ā€“ š‘— Ģ‚ + 2š‘˜ Ģ‚ Area of the parallelogram = 1/2 |š‘Ž āƒ—Ć—š‘ āƒ— | Finding š’‚ āƒ— Ɨ š’ƒ āƒ— š‘Ž āƒ— Ɨ š‘ āƒ— = |ā– 8(š‘– Ģ‚&š‘— Ģ‚&š‘˜ Ģ‚@2&āˆ’3&4@2&āˆ’1&2)| = š‘– Ģ‚ ((ā€“3) Ɨ 2 ā€“ (-1) Ɨ 4) āˆ’ š‘— Ģ‚ (2 Ɨ 2 āˆ’ 2 Ɨ 4) + š‘˜ Ģ‚ (2 Ɨ (-1) āˆ’ 2 Ɨ (-3)) = š‘– Ģ‚ (-6 + 4) āˆ’ š‘— Ģ‚ (4 ā€“ 8) + š‘˜ Ģ‚ (ā€“2 + 6) = š‘– Ģ‚ (āˆ’2) - š‘— Ģ‚ (āˆ’4) + š‘˜ Ģ‚ (4) = ā€“2š‘– Ģ‚ + 4š‘— Ģ‚ + 4š‘˜ Ģ‚ So, Magnitude of š‘Ž āƒ— Ɨ š‘ āƒ— = āˆš((āˆ’2)2+(4)2+(4)2) |š‘Ž āƒ—" Ɨ " š‘ āƒ— | = āˆš(4+16+16) |š‘Ž āƒ—" Ɨ " š‘ āƒ— |= āˆš36 |š‘Ž āƒ—" Ɨ " š‘ āƒ— |= 6 Thus, Area of the parallelogram = 1/2 |š‘Ž āƒ—Ć—š‘ āƒ— | = 1/2 Ɨ 6 = 3 square units

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.