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,


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