Let the lines l₁: (x+5)/3=(y+4)/1=(z-α)/(-2) and l₂: 3 x+2 y+z-2=0=x-3 y+2 z-13 be coplanar. If the point P(a, b, c) on l₁ is nearest to the point Q(-4,-3,2), then |a|+|b|+|c| is equal to

Three Dimensional Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 12 Apr, Morning shift · Q2517

JEE Main 202312 Apr, Morning shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let the lines

l_{1}: \frac{x+5}{3}=\frac{y+4}{1}=\frac{z-\alpha}{-2}

and

l_{2}: 3 x+2 y+z-2=0=x-3 y+2 z-13

be coplanar. If the point

\mathrm{P}(a, b, c)

l_{1}

is nearest to the point

\mathrm{Q}(-4,-3,2)

, then

|a|+|b|+|c|

is equal to