Direction cosines of the line passing through the points `A(-4, 2, 3) and B(1, 3, -2)` are

Options

A. `pm(1)/(sqrt(51)),pm(5)/(sqrt(51)),pm(1)/(sqrt(51))`
B. `pm(5)/(sqrt(51)),pm(1)/(sqrt(51)),pm(-5)/(sqrt(51))`
C. `pm5,pm1,pm5`
D. `pmsqrt(51)msqrt(51),pmsqrt(51)`

Answer

B

Explanation

Given, points are `A-=(-4,2,3) and B-=(1,3,-2)`
`1-(-4),3-2,-2-3` i.e., `5,1,-5`
`therefore" "` The direction cosines of AB are
`=pm(5)/(sqrt(5^(2)+1^(2)+(-5)^(2))), pm(1)/(sqrt(5^(2)+1^(2)+(-5)^(2))),pm(-5)/(sqrt(5^(2)+1^(2)+(-5)^(2)))`
`=pm(5)/(sqrt(51)),pm(1)/(sqrt(51)),pm(-5)/(sqrt(51))`.