Ex 10.2, 14 - Show that i + j + k is equally inclined to OX, OY

Ex 10.2, 14 - Chapter 10 Class 12 Vector Algebra - Part 2

  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise

Transcript

Ex 10.2, 14 Show that the vector ๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚ is equally inclined to the axes OX, OY and OZ. Let ๐‘Ž โƒ— = ๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚ = 1๐‘– ฬ‚ + 1๐‘— ฬ‚ + 1๐‘˜ ฬ‚ A vector is equally inclined to OX, OY, OZ i.e. X, Y and Z axes respectively, if its direction cosines are equal. Direction ratios of ๐‘Ž โƒ— are ๐‘Ž = 1, b = 1 , c = 1 Magnitude of ๐‘Ž โƒ— = โˆš(12+12+12) |๐‘Ž โƒ— | = โˆš(1+1+1) = โˆš3 Direction cosines OF ๐‘Ž โƒ— are (๐‘Ž/|๐‘Ž โƒ— | ,๐‘/|๐‘Ž โƒ— | ,๐‘/|๐‘Ž โƒ— | ) = (1/โˆš3,1/โˆš3,1/โˆš3) Since the direction cosines are equal, ๐‘Ž โƒ— = ๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚ is equally inclined to OX, OY and OZ

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.