Let a line L be perpendicular to both the lines L₁:(x+1)/3=(y+3)/5=(z+5)/7 and L₂:(x-2)/1=(y-4)/4=(z-6)/7. If θ is the acute angle between the lines L and L₃:(x-8/7)/2=(y-4/7)/1=z/2, then tan θ is equal to:

Three Dimensional Geometry: JEE Main 2026 Mathematics question

JEE Main 2026 · 6 Apr, Morning shift · Q16

JEE Main 20266 Apr, Morning shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let a line L be perpendicular to both the lines

L_1:\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}

and

L_2:\frac{x-2}{1}=\frac{y-4}{4}=\frac{z-6}{7}

. If

\theta

is the acute angle between the lines L and

L_3:\frac{x-\frac87}{2}=\frac{y-\frac47}{1}=\frac{z}{2}

, then

\tan\theta

is equal to: