Check sibling questions

Ex 10.2, 9 - For a = 2i - j + 2k, and b = -i + j - k, find unit vector

Ex 10.2, 9 - Chapter 10 Class 12 Vector Algebra - Part 2

This video is only available for Teachoo black users

Introducing your new favourite teacher - Teachoo Black, at only β‚Ή83 per month


Transcript

Ex 10.2, 9 For given vectors, π‘Ž βƒ— = 2𝑖 Μ‚ βˆ’ 𝑗 Μ‚ + 2π‘˜ Μ‚ and 𝑏 βƒ— = βˆ’π‘– Μ‚ + 𝑗 Μ‚ βˆ’ π‘˜ Μ‚ , find the unit vector in the direction of the vector π‘Ž βƒ— + 𝑏 βƒ—π‘Ž βƒ— = 2𝑖 Μ‚ βˆ’ j Μ‚ + 2π‘˜ Μ‚ = 2𝑖 Μ‚ – 1𝑗 Μ‚ + 2π‘˜ Μ‚ 𝑏 βƒ— = βˆ’π‘– Μ‚ + 𝑗 Μ‚ – π‘˜ Μ‚ = βˆ’1𝑖 Μ‚ + 1𝑗 Μ‚ – 1π‘˜ Μ‚ Now, (π‘Ž βƒ— + 𝑏 βƒ—) = (2 – 1) 𝑖 Μ‚ + (-1 + 1) 𝑗 Μ‚ + (2 – 1) π‘˜ Μ‚ = 1𝑖 Μ‚ + 0𝑗 Μ‚ + 1π‘˜ Μ‚ Let 𝑐 βƒ— = π‘Ž βƒ— + 𝑏 βƒ— ∴ c βƒ— = 1𝑖 Μ‚ + 0𝑗 Μ‚ + 1π‘˜ Μ‚ Magnitude of 𝑐 βƒ— = √(12+02+12) |𝑐 βƒ— | = √(1+0+1) = √2 Unit vector in direction of 𝑐 βƒ— = 1/|𝑐 βƒ— | . 𝑐 βƒ— 𝑐 Μ‚ = 1/√2 [1𝑖 Μ‚+0𝑗 Μ‚+1π‘˜ Μ‚ ] 𝑐 Μ‚ = 1/√2 𝑖 Μ‚ + 0𝑗 Μ‚ + 1/√2 π‘˜ Μ‚ 𝑐 Μ‚ = 𝟏/√𝟐 π’Š Μ‚ + 𝟏/√𝟐 π’Œ Μ‚ Thus, unit vector in direction of 𝑐 βƒ— = 1/√2 𝑖 Μ‚ + 1/√2 π‘˜ Μ‚

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.