Let a line passing through the point (4,1,0) intersect the line L₁: (x-1)/2=(y-2)/3=(z-3)/4 at the point A(α,β,γ) and the line L₂: x-6 = y - z + 4 at the point B(a,b,c). Then det 1 0 1 α β γ a b c is equal to:

Three Dimensional Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q77

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumThree Dimensional Geometry249× since 2002

Let a line passing through the point

(4,1,0)

intersect the line

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

at the point

A(\alpha,\beta,\gamma)

and the line

L_2:\;x-6 = y - z + 4

at the point

B(a,b,c)

. Then

\det\begin{pmatrix}1 & 0 & 1 \\ \alpha & \beta & \gamma \\ a & b & c\end{pmatrix}

is equal to:

JEE Main 2025 Three Dimensional Geometry Question with Solution (April Unspecified (session-level dataset), Q77) | JEE Arc

JEE Main 2025 · April, Unspecified (session-level dataset) · Q77

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumThree Dimensional Geometry249× since 2002

Let a line passing through the point

(4,1,0)

intersect the line

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

at the point

A(\alpha,\beta,\gamma)

and the line

L_2:\;x-6 = y - z + 4

at the point

B(a,b,c)

. Then

\det\begin{pmatrix}1 & 0 & 1 \\ \alpha & \beta & \gamma \\ a & b & c\end{pmatrix}

is equal to: