Last updated at May 29, 2018 by Teachoo

Transcript

Misc 7 If 𝑎 = 𝑖 + 𝑗 + 𝑘, 𝑏 = 2 𝑖 − 𝑗 + 3 𝑘 and 𝑐 = 𝑖 − 2 𝑗 + 𝑘 , find a unit vector parallel to the vector 2 𝑎 – 𝑏 + 3 𝑐 . 𝑎 = 𝑖 + 𝑗 + 𝑘 = 1 𝑖 −1 𝑗 + 1 𝑘 𝑏 = 2 𝑖 + 𝑗 + 3 𝑘 = 2 𝑖 −1 𝑗 + 3 𝑘 𝑐 = 𝑖 − 2 𝑗 + 𝑘 = 1 𝑖 −2 𝑗 + 1 𝑘 Let 𝑟 = 2 𝑎 − 𝑏 + 3 𝑐 = 2(1 𝑖 −2 𝑗 + 1 𝑘) − (2 𝑖 − 1 𝑗 + 3 𝑘) + 3(1 𝑖 −2 𝑗 + 1 𝑘) = 2 𝑖 − 1 𝑗 + 2 𝑘 − 2 𝑖 − 1 𝑗 + 3 𝑘 + 3 𝑖 − 6 𝑗 + 3 𝑘 = (2 − 2 + 3) 𝑖 + (2 + 1 − 6) 𝑗 + (2 − 3 + 3) 𝑘 = 3 𝑖 – 3 𝑗 + 2 𝑘 ∴ 𝒓 = 3 𝒊 – 3 𝒋 + 2 𝒌 Magnitude of 𝑟 = 32+ −32+22 𝑟 = 9+9+4 = 22 Unit vector in the direction of 𝑟 = 1 𝑟 x 𝑟 = 1 22 × 3 𝑖 −3 𝑗+2 𝑘 = 3 22 𝑖 – 3 22 𝑗 + 2 22 𝑘 Hence the required vector is 𝟑 𝟐𝟐 𝒊 – 𝟑 𝟐𝟐 𝒋 + 𝟐 𝟐𝟐 𝒌

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.