The line L₁ is parallel to the vector a = -3i + 2j + 4k and passes through the point (7, 6, 2) and the line L₂ is parallel to the vector b = 2i + j + 3k and passes through the point (5, 3, 4). The shortest distance between the lines L₁ and L₂ is:

Three Dimensional Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q6

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

The line

L_1

is parallel to the vector

\vec{a} = -3\hat{i} + 2\hat{j} + 4\hat{k}

and passes through the point

(7, 6, 2)

and the line

L_2

is parallel to the vector

\vec{b} = 2\hat{i} + \hat{j} + 3\hat{k}

and passes through the point

(5, 3, 4)

. The shortest distance between the lines

L_1

and

L_2

is:

JEE Main 2025 · April, Unspecified (session-level dataset) · Q6

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

The line

L_1

is parallel to the vector

\vec{a} = -3\hat{i} + 2\hat{j} + 4\hat{k}

and passes through the point

(7, 6, 2)

and the line

L_2

is parallel to the vector

\vec{b} = 2\hat{i} + \hat{j} + 3\hat{k}

and passes through the point

(5, 3, 4)

. The shortest distance between the lines

L_1

and

L_2

is: