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

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Revise Equation of a line; Skew lines, the shortest distance between them and its equation by covering every subtopic once, drilling formulas, then solving 8+ timed MCQs with full solutions.

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Revision checklist

  1. 1.Core idea: Equation of a line; Skew lines, the shortest distance between them and its equation
  2. 2.Relates to other subtopics in Three Dimensional Geometry
  3. 3.Direction ratios and cosines
  4. 4.Equation of line in 3D
  5. 5.Master Equation of a line; Skew lines, the shortest distance between them and its equation definitions and standard results
  6. 6.Solve 20 timed MCQs for Equation of a line; Skew lines, the shortest distance between them and its equation

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 x+y+z=6\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{6} and 2x+3y+4z+5=\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}+\boldsymbol{4} \boldsymbol{z}+\boldsymbol{5}= 0,0, and the point (1,1,1) is
Q2MathsUnit 11: Three Dimensional Geometry
Find the equation of the plane through the points A(2,2−1),B(3,4,2)\boldsymbol{A}(\mathbf{2}, \mathbf{2}-\mathbf{1}), \boldsymbol{B}(\mathbf{3}, \mathbf{4}, \mathbf{2}) and C(7,0,6)\boldsymbol{C}(\boldsymbol{7}, \boldsymbol{0}, \boldsymbol{6})
Q3MathsUnit 11: Three Dimensional Geometry
x−21=y−31=z−4−1&x−1k=\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-1} \& \frac{x-1}{k}= y−42=z−52\frac{\boldsymbol{y}-\boldsymbol{4}}{\boldsymbol{2}}=\frac{\boldsymbol{z}-\boldsymbol{5}}{\boldsymbol{2}} are coplanar then k=?\mathbf{k}=?
Q4MathsUnit 11: Three Dimensional Geometry
The shortest distance between the lines x−54=y−7−5=z+3−5\frac{\boldsymbol{x}-\mathbf{5}}{\mathbf{4}}=\frac{\boldsymbol{y}-\mathbf{7}}{-\mathbf{5}}=\frac{\boldsymbol{z}+\mathbf{3}}{-\mathbf{5}} and x−84=\frac{\boldsymbol{x}-\mathbf{8}}{\mathbf{4}}= y−7−5=z−5−5\frac{y-7}{-5}=\frac{z-5}{-5} is
Q5MathsUnit 11: Three Dimensional Geometry
If the points (x,y,−3),(2,0,−1)(x, y,-3),(2,0,-1) and (4,2,3) lies on a straight line, then what are the values of xx and yy respectively?
Q6MathsUnit 11: Three Dimensional Geometry
If the distance between a point PP and the point (1,1,1) on the line x−13=\frac{x-1}{3}= y−14=z−112\frac{y-1}{4}=\frac{z-1}{12} is 13,13, then the coordinates of PP are
Q7MathsUnit 11: Three Dimensional Geometry
The foot of the perpendicular from the point A(7,14,5)\boldsymbol{A}(\mathbf{7}, \mathbf{1 4}, \mathbf{5}) to the plane 2x+4y−\mathbf{2} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}- z=2z=2 is?
Q8MathsUnit 11: Three Dimensional Geometry
A line d.c's proportional to (2,1,2) meets each of the lines x=y+a=z\boldsymbol{x}=\boldsymbol{y}+\boldsymbol{a}=\boldsymbol{z} and x+a=2y=2z.x+a=2 y=2 z . Then the coordinates of each of the points of intersection are given by

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Follow the checklist on this page, revise formulas daily, and attempt mixed MCQs every 2–3 days.

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