If the angle between the line `x(y-1)/2=(z-3)/lamda ` and the plane `x+2y+3z=4` is `cos^-1 (sqrt(5/14)), then lamda=`

Options

A. `(3)/(2)`
B. `(2)/(5)`
C. `(5)/(3)`
D. `(2)/(3)`

Answer

D

Explanation

Here, `a_(1)=1,b_(1)=2,c_(1)=lamda`
`and" "a_(2)=1,b_(2)=2,c_(2)=3`
`:." "sintheta=(1xx1+2xx2+lamdaxx3)/(sqrt(1+4+lamda^(2))sqrt(1+4+9))`
`rArr" "sintheta=(5+3lamda)/(sqrt(lamda^(2)+5)*sqrt(14))` . . .(i)
`:." "sintheta=(3)/(sqrt(14))rArr(3)/(sqrt(14))=(5+3lamda)/(sqrt(lamda^(2)+5)*sqrt(14))`
`rArr" "9(lamda^(2)+5)=9lamda^(2)+30lamda+25`
`rArr" "30lamda=20rArrlamda=(2)/(3)`