Mathematics · JEE

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

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Q1MathsUnit 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})

Q2MathsUnit 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}

Q3MathsUnit 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?

Q4MathsUnit 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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