If the distance between the origin O and point P is `5` units and the direction ratios of line segment are `(1,-2,3)` then the coordinates of P are

Options

A. `(5/sqrt(14),(-10)/(sqrt14),(15)/sqrt14)`
B. `(5/sqrt(14),(10)/(sqrt14),(15)/sqrt14)`
C. `((-5)/sqrt(14),(-10)/(sqrt14),(-15)/sqrt14)`
D. None of these

Answer

A

Explanation

Given (a,b,c) = (1,-2,3)
Now `sqrt(a^2+b^2+c^2)=sqrt(a^2+(-2)^2+3^2)=sqrt(14)`
`therefore" "(l,m,n) = (1/sqrt(14),(-2)/sqrt(14),3/sqrt(14))`
Also, given r=5
`therefore` Coordinate of P are (lr,mr,nr)
`=(1/sqrt(14)xx5,(-2)/sqrt(14)xx5,3/sqrt(14)xx5)`
`=(5/sqrt(14),(-10)/sqrt(14),(15)/sqrt(14))`