Question

What are the cosines of the angles a, p, 6 between the vector (1,0, — 1) and the unit
vectors i, j ,k along the axes? Check the formula cos
2
a 4- cos
2
§ 4- cos
2
0 = 1

Answer 1

page 20,chapter 1, exercise 17

Answer 2

check the formula cos^2a+cos^2b+cos^2θ=1

Answer 3

you looking for the cosine of angle between two vectors: your vector let us call it V and one of unit vectors i,j or k.
by using dot product formula
\[|V| = \sqrt{1^2+0^2+(-1)^2} = \sqrt{2}.\]
\[\cos(\alpha) = V.i /|V||i| = 1/\sqrt{2}.\]
\[\cos(\beta) = V.j /|V||j| = 0.\]
\[\cos(\gamma) = V.k /|V||k| = -1/\sqrt{2}\]

you can verify the formula \[\cos ^2(\alpha) + \cos ^2(\beta) + \cos ^2(\gamma) = 1\]
\[V.V/|V|^2 = 1. \] #