If the line `(x-1)/(2)=(y+1)/(3)=(z-2)/(4)` meets the plane, `x+2y+3z=15` at a point P, then the distance of P from the origin isA. `7//2`B. `9//2`C. `sqrt(5)//2`D. `2sqrt(5)`

If the line `(x-1)/(2)=(y+1)/(3)=(z-2)/(4)` meets the plane, `x+2y+3z=

1.	If the line `(x-1)/(2)=(y+1)/(3)=(z-2)/(4)` meets the plane, `x+2y+3z=15` at a point P, then the distance of P from the origin isA. `7//2`B. `9//2`C. `sqrt(5)//2`D. `2sqrt(5)`
Answer» Correct Answer - B Equation of given plane is `x+2y+3z=15" "...(i)` and line is, `(x-1)/(2)=(y+1)/(3)=(z-2)/(4)=r("let")" "...(ii)` So, the coordinates of any point on line (ii) is `P(1+2r,-1+3r,2+4r)`. `because` Point P is intersecting point of plane (i) and line (ii) `:.(1+2r)+2(-1+3r)+3(2+4r)=15` `implies1+2r-2+6r+6+12r=15implies20r=10` `impliesr=(1)/(2)` `:.` Coordinates of `P=(1+1,-1+(3)/(2),2+2)=(2,(1)/(2),4)` Now, distance of the point P from the origin `=sqrt(4+(1)/(4)+16)=sqrt(20+(1)/(4))=sqrt((81)/(4))=(9)/(2)` units

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If the line `(x-1)/(2)=(y+1)/(3)=(z-2)/(4)` meets the plane, `x+2y+3z=15` at a point P, then the distance of P from the origin isA. `7//2`B. `9//2`C. `sqrt(5)//2`D. `2sqrt(5)`

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