Mathematics · JEE

Equation of a line; Skew lines, the shortest distance between them and its equation Concepts for JEE

8+ syllabus-aligned questions available

Quick answer

Master Equation of a line; Skew lines, the shortest distance between them and its equation by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

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Concept explainer

Equation of a line; Skew lines, the shortest distance between them and its equation is a core JEE Main Mathematics subtopic under Three Dimensional Geometry. Master the definitions, standard results, and typical MCQ patterns tested in JEE Main and Advanced.

Key points

Understand the definition and scope of Equation of a line; Skew lines, the shortest distance between them and its equation in the JEE syllabus
Memorise key formulas and standard results linked to Equation of a line; Skew lines, the shortest distance between them and its equation
Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

Revise Equation of a line; Skew lines, the shortest distance between them and its equation with a one-page formula sheet before attempting mixed tests
After each practice set, log mistakes specific to Equation of a line; Skew lines, the shortest distance between them and its equation and reattempt after 48 hours

Common trap

Students often rush Equation of a line; Skew lines, the shortest distance between them and its equation questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

Syllabus context

Part of Three Dimensional Geometry in JEE Main Mathematics.

Free sample questions

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Q1MathsUnit 11: Three Dimensional Geometry

The equation of the plane passing through the intersection of the planes

\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{6}

and

\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}+\boldsymbol{4} \boldsymbol{z}+\boldsymbol{5}=

0,

and the point (1,1,1) is

Q2MathsUnit 11: Three Dimensional Geometry

Find the equation of the plane through the points

\boldsymbol{A}(\mathbf{2}, \mathbf{2}-\mathbf{1}), \boldsymbol{B}(\mathbf{3}, \mathbf{4}, \mathbf{2})

and

\boldsymbol{C}(\boldsymbol{7}, \boldsymbol{0}, \boldsymbol{6})

Q3MathsUnit 11: Three Dimensional Geometry

\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-1} \& \frac{x-1}{k}=

\frac{\boldsymbol{y}-\boldsymbol{4}}{\boldsymbol{2}}=\frac{\boldsymbol{z}-\boldsymbol{5}}{\boldsymbol{2}}

are coplanar then

\mathbf{k}=?

Q4MathsUnit 11: Three Dimensional Geometry

The shortest distance between the lines

\frac{\boldsymbol{x}-\mathbf{5}}{\mathbf{4}}=\frac{\boldsymbol{y}-\mathbf{7}}{-\mathbf{5}}=\frac{\boldsymbol{z}+\mathbf{3}}{-\mathbf{5}}

and

\frac{\boldsymbol{x}-\mathbf{8}}{\mathbf{4}}=

\frac{y-7}{-5}=\frac{z-5}{-5}

Q5MathsUnit 11: Three Dimensional Geometry

If the points

(x, y,-3),(2,0,-1)

and (4,2,3) lies on a straight line, then what are the values of

x

and

y

respectively?

Q6MathsUnit 11: Three Dimensional Geometry

If the distance between a point

P

and the point (1,1,1) on the line

\frac{x-1}{3}=

\frac{y-1}{4}=\frac{z-1}{12}

13,

then the coordinates of

P

are

Q7MathsUnit 11: Three Dimensional Geometry

The foot of the perpendicular from the point

\boldsymbol{A}(\mathbf{7}, \mathbf{1 4}, \mathbf{5})

to the plane

\mathbf{2} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}-

z=2

is?

Q8MathsUnit 11: Three Dimensional Geometry

A line d.c's proportional to (2,1,2) meets each of the lines

\boldsymbol{x}=\boldsymbol{y}+\boldsymbol{a}=\boldsymbol{z}

and

x+a=2 y=2 z .

Then the coordinates of each of the points of intersection are given by

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Frequently asked questions

What concepts in Equation of a line; Skew lines, the shortest distance between them and its equation are essential for JEE?

Focus on core ideas across Equation of a line; Skew lines, the shortest distance between them and its equation. JEE tests application, not just memorisation.