Question

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

(i) vectors (i - j + k)

(ii) vectors (j +- k)

(iii) vectors (i - 4j + 8k)

Answer 1

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

 cosθ = \(\frac{R_1.R_2}{|R_1||R_2|}\)

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

Hence,θ = cos^-1(\(\frac{1}{\sqrt{3}}\))

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

  cosθ = \(\frac{R_1.R_2}{|R_1||R_2|}\)

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

So, here we have,

R₁ = j - k and R₂ = i for x- axis

Hence,θ = \(\frac{3\pi}{4}\)

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

   cosθ = \(\frac{R_1.R_2}{|R_1||R_2|}\)

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