The ratio in which the line segment joining the points whose position vectors are `2hati-4hatj-7hatkand-3hati+5hatj-8hatk` is divided by the plane whose equation is `hatr.(hati-2hatj+3hatk)=13`is

Options

A. 13:12 internally
B. 12:25 externally
C. 13:25 internally
D. 37:25 internally

Answer

b

Explanation

Let P be the point and it divides the line segment in the ratio `lamda :1 `. Then,
`" "vec(OP)=vecr= (-3lamda+2)/(lamda+1)hati+ (5lamda-4)/(lamda+1)hatj+ (-8lamda-7)/(lamda+1)hatk`
It satisfies `vecr*(hati-2hatj+3hatk)= 13`. So,
`" "(-3lamda+2)/(lamda+1)-2(5lamda-4)/(lamda+1)+3(-8lamda-7)/(lamda+1)=13`
or `" "-3lamda+2-2(5lamda-4)+3(-8lamda-7)= 13 (lamda+1)`
or `" "-37lamda-11=13lamda+13 or 50 lamda= -24 or lamda= - (12)/(25)`