Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 8 The Cartesian equation of a line is 𝑥 + 32 = 𝑦 − 54 = 𝑧 + 62 Find the vector equation for the line. Cartesian equation : 𝑥 + 32 = 𝑦 − 54 = 𝑧 + 62 𝑥 − (− 3)2 = 𝑦 − 54 = 𝑧 − (− 6)2 Equation of a line in Cartesian form is 𝑥 − 𝑥1𝑎 = 𝑦 − 𝑦1𝑏 = 𝑧 − 𝑧1𝑐 Comparing (1) and (2), 𝑥1= −3, 𝑦1= 5, 𝑧1= −6 & 𝑎 = 2, 𝑏 = 4, c = 2 Equation of line in vector form is 𝑟 = 𝑎 + 𝜆 𝑏 where 𝑎 = 𝑥1 𝑖 + y1 𝑗 + z1 𝑘 = − 3 𝑖 + 5 𝑗 − 6 𝑘 & 𝑏 = 𝑎 𝑖 + b 𝑗 + c 𝑘 = 2 𝑖 + 4 𝑗 + 2 𝑘 Now, 𝑟 = ( −3 𝒊 + 5 𝒋 − 6 𝒌) + 𝜆 (2 𝒊 + 4 𝒋 + 2 𝒌) Therefore, equation of line in vector form is ( −3 𝑖 + 5 𝑗 − 6 𝑘) + 𝜆 (2 𝑖 + 4 𝑗 + 2 𝑘)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can contact him here.