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If š‘Ž āƒ— ā‰  0 āƒ—, š‘Ž āƒ—. š‘ āƒ— = š‘Ž āƒ—. š‘ āƒ—, š‘Ž āƒ— Ɨ š‘ āƒ— = š‘Ž āƒ— Ɨ š‘ āƒ— , then show that š‘ āƒ— = š‘ āƒ—.

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Question 9 If š‘Ž āƒ— ā‰  0 āƒ—, š‘Ž āƒ—. š‘ āƒ— = š‘Ž āƒ—. š‘ āƒ—, š‘Ž āƒ— Ɨ š‘ āƒ— = š‘Ž āƒ— Ɨ š‘ āƒ— , then show that š‘ āƒ— = š‘ āƒ—. Given that š’‚ āƒ—. š’ƒ āƒ— = š’‚ āƒ—. š’„ āƒ— Now, š‘Ž āƒ—. š‘ āƒ— = š‘Ž āƒ—. š‘ āƒ— š‘Ž āƒ—. š‘ āƒ— āˆ’ š‘Ž āƒ—. š‘ āƒ— = 0 š’‚ āƒ—. (š’ƒ āƒ— āˆ’ š’„ āƒ—) = 0 Thus, either (š’ƒ āƒ— āˆ’ š’„ āƒ—) = šŸŽ āƒ— Or š’‚ āƒ— is perpendicular to (š’ƒ āƒ— āˆ’ š’„ āƒ—) š’‚ āƒ— Ɨ š’ƒ āƒ— = š’‚ āƒ— Ɨ š’„ āƒ— Now, š‘Ž āƒ— Ɨ š‘ āƒ— = š‘Ž āƒ— Ɨ š‘ āƒ— š‘Ž āƒ— Ɨ š‘ āƒ— āˆ’ š‘Ž āƒ— Ɨ š‘ āƒ— = šŸŽ āƒ— š’‚ āƒ— Ɨ (š’ƒ āƒ— āˆ’ š’„ āƒ—) = šŸŽ āƒ— Thus, either (š’ƒ āƒ— āˆ’ š’„ āƒ—) = šŸŽ āƒ— Or š’‚ āƒ— is parallel to (š’ƒ āƒ— āˆ’ š’„ āƒ—) Since š‘Ž āƒ— cannot both be perpendicular and parallel to (š‘ āƒ— āˆ’ š‘ āƒ—) Therefore, the only other solution is (š‘ āƒ— āˆ’ š‘ āƒ—) = 0 āƒ— š’ƒ āƒ— = š’„ āƒ— Hence proved

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Davneet Singh

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.