Find the angles made by the following vectors with the coordinate axes:

(i)

(ii)

(iii)

(i) The angle between the two lines is given by

cos =

where R₁ and R₂ denote the vectors with the direction ratios,

So, here we have,

R1 = i - j + k and R2 = i for x- axis

cos =

cos

Hence,

With y- axis, i. e. R2 = j

cos =

cos

Hence,

With z- axis, i. e. R2 = k

cos =

cos

Hence,

(ii) The angle between the two lines is given by

cos =

where R₁ and R₂ denote the vectors with the direction ratios,

So, here we have,

R1 = j - k and R2 = i for x- axis

cos =

cos

Hence,

With y- axis, i. e. R2 = j

cos =

cos

Hence,

With z- axis, i. e. R2 = k

cos =

cos

Hence,

(iii) The angle between the two lines is given by

cos =

where R₁ and R₂ denote the vectors with the direction ratios,

So, here we have,

R1 = i - 4j + 8k and R2 = i for x- axis

cos =

cos

Hence,

With y- axis, i. e. R2 = j

cos =

cos

Hence,

With z- axis, i. e. R2 = k

cos =

cos

Hence,