If the lines (x-k)/(1)=(y-2)/(2)=(z-3)/(3) and (x+1)/(3)=(y+2)/(2)=(z+3)/(1) are co-planar, then the value of k is \_\_\_\_\_\_ .

3D Geometry: If the lines (x-k)/(1)=(y-2)/(2)=(z-3)/(3) and… | JEE Main 2021

JEE Main 2021 (Online) 25th July Evening ShiftQuestion 1

If the lines $\frac{x-k}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x+1}{3}=\frac{y+2}{2}=\frac{z+3}{1}$ are co-planar, then the value of $k$ is $\_\_\_\_\_\_$ .

3D Geometry

Answer$1$

Solution

Points $(k,2,3)$, $(-1,-2,-3)$; dirs $(1,2,3)$, $(3,2,1)$. $d_1\times d_2=(-4,8,-4)$. Coplanar: $(-1-k,-4,-6)\cdot(-4,8,-4)=4+4k-32+24=4k-4=0\Rightarrow k=1$.

3D Geometry - JEE Mathematics question (JEE Main 2021 (Online) 25th July Evening Shift)

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