Last updated at March 11, 2017 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

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

Example 11

Example 12

Example 13

Example 14 Important

Example 15

Example 16 Important

Example 17

Example 18

Example 19

Example 20

Example 21 Important

Example 22

Example 23 Important

Example 24 Important

Example 25 Important

Example 26

Example 27

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 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.