Question

Find the direction cosines of a line segment whose direction ratios are:

(i) 2, -6, 3

(ii) 2, -1, -2

(iii) -9, 6, -2

Answer 1

(i) It is given that

Direction ratios (2,-6,3)

Consider (1,m,n) as the direction cosines where 1² + m² + n² = 1

Hence, the direction cosines are (2/7,-6/7,3/7)

(ii) It is given that

Direction ratios (2,-1,-2)

Consider (1,m,n) as the direction cosines where 1² + m² + n² = 1

Hence, the direction cosines are (2/3,-1/3,-2/3)

(iii) It is given that

Direction ratios (-9,6,-2)

Consider (1,m,n) as the direction cosines where 1² + m² + n² = 1

Hence, the direction cosines are (-9/11,6/11,-2/11)