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

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Hard Equation of a line; Skew lines, the shortest distance between them and its equation MCQs train multi-concept problem solving — attempt after mastering easy and medium sets (13+ on Goodmarks).

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Part of Three Dimensional Geometry in JEE Main Mathematics.

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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

The equation of a plane passing through the point

A(2,-3,7)

and making equal intercepts on the axes, is?

Q7MathsUnit 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

Q8MathsUnit 11: Three Dimensional Geometry

A plane which passes through the point (3,2,0) and the line

\frac{x-3}{1}=\frac{y-7}{5}=

\frac{z-4}{4}

is?

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