If the distances of the point (1,2,a) from the line (x-1)/1=y/2=(z-1)/1 along the lines L₁:(x-1)/3=(y-2)/4=(z-a)/b and L₂:(x-1)/1=(y-2)/4=(z-a)/c are equal, then a+b+c is equal to

Three Dimensional Geometry: JEE Main 2026 Mathematics question

JEE Main 2026 · 28 Jan, Morning shift · Q3

JEE Main 202628 Jan, Morning shiftMathematicsMediumThree Dimensional Geometry249× since 2002

If the distances of the point

(1,2,a)

from the line

\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}

along the lines

L_1:\frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b}

and

L_2:\frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c}

are equal, then

a+b+c

is equal to