Last updated at May 29, 2018 by Teachoo

Transcript

Example 28 Let 𝑎, 𝑏 and 𝑐 be three vectors such that | 𝑎|= 3, | 𝑏|= 4, | 𝑐|= 5 and each one of them being perpendicular to the sum of the other two, find 𝑎 + 𝑏 + 𝑐. Given, | 𝑎| = 3 , | 𝑏| = 4 , | 𝑐|= 5 Also, each one of them being perpendicular to the sum of the other two 𝒂 is perpendicular to 𝒃 + 𝒄 i.e. 𝑎. ( 𝑏 + 𝑐) = 0 ⇒ 𝒂. 𝒃 + 𝒂. 𝒄 = 0 𝒃 is perpendicular to 𝒂 + 𝒄 i.e. 𝑏. ( 𝑎 + 𝑐) = 0 ⇒ 𝒃. 𝒂 + 𝒃. 𝒄 = 0 𝒄 is perpendicular to 𝒂 + 𝒃 i.e. 𝑐. ( 𝑎 + 𝑏) = 0 ⇒ 𝒄. 𝒂 + 𝒄. 𝒃 = 0 Now, | 𝒂+ 𝒃+ 𝒄 |2 = ( 𝒂 + 𝒃 + 𝒄) . ( 𝒂 + 𝒃 + 𝒄) = 𝑎. 𝑎 + 𝑎 . 𝑏 + 𝑎 . 𝑐 + 𝑏 . 𝑎 + 𝑏 . 𝑏 + 𝑏 . 𝑐 + 𝑐 . 𝑎 + 𝑐 . 𝑏 + 𝑐 . 𝑐 = 𝑎. 𝑎 + ( 𝒂 . 𝒃 + 𝒂 . 𝒄) + 𝑏 . 𝑏 + ( 𝒃 . 𝒂 + 𝒃 . 𝒄) + 𝑐 . 𝑐 + ( 𝒄 . 𝒂 + 𝒄 . 𝒃) = 𝑎. 𝑎 + (0) + 𝑏 . 𝑏 + (0) + 𝑐 . 𝑐 + (0) = 𝒂. 𝒂 + 𝑏. 𝑏 + 𝑐. 𝑐 = | 𝒂|2 + | 𝑏|2 + | 𝑐|2 = 32 + 42 + 52 = 9 + 16 + 25 = 50 So, | 𝑎+ 𝑏+ 𝑐 |2 = 50 Taking square root both sides, | 𝑎 + 𝑏 + 𝑐| = 50 | 𝑎 + 𝑏 + 𝑐| = 25 x 2 | 𝑎 + 𝑏 + 𝑐| = 5 2 So, | 𝒂 + 𝒃 + 𝒄| = 𝟓 𝟐

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Example 28 Important You are here

Example 29 Important

Example 30 Important

Example 26 (Supplementary NCERT)

Example 27 (Supplementary NCERT)

Example 28 (Supplementary NCERT)

Example 29 (Supplementary NCERT)

Example 30 (Supplementary NCERT)

Example 31 (Supplementary NCERT)

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.