Skew Lines and Coplanar Lines
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Three Dimensional Geometry

121226 Let \(\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z+3}{-1}\) lie on the plane \(p x-q y\) \(+z=5\), for some \(p, q \in R\). The shortest distance of the plane from the origin is :

1 \(\sqrt{\frac{3}{109}}\)
2 \(\sqrt{\frac{5}{142}}\)
3 \(\sqrt{\frac{5}{71}}\)
4 \(\sqrt{\frac{1}{142}}\)
JEE Main-29.06.2022
Three Dimensional Geometry

121227 The shortest distance between the lines \(\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}\) and \(\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}\) is

1 \(2 \sqrt{3}\)
2 \(5 \sqrt{3}\)
3 \(4 \sqrt{3}\)
4 \(3 \sqrt{3}\)
JEE Main-29.01.2023
Three Dimensional Geometry

121229 Let the plane \(P: 8 x+\alpha_1 y+\alpha_2 z+12=0\) be parallel to the line \(\frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{5}\). If the intercept of \(P\) on the \(y\)-axis is 1 , then the distance between \(P\) and \(L\) is

1 \(\sqrt{\frac{2}{7}}\)
2 \(\frac{6}{\sqrt{14}}\)
3 \(\sqrt{\frac{7}{2}}\)
4 \(\sqrt{14}\)
JEE Main-31.01.2023
Three Dimensional Geometry

121230 The shortest distance between the lines \(\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}\) and \(\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0}\) is

1 6
2 9
3 7
4 8
JEE Main-10.04.2023
NEET DIGITAL LIBRARY
Three Dimensional Geometry

121226 Let \(\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z+3}{-1}\) lie on the plane \(p x-q y\) \(+z=5\), for some \(p, q \in R\). The shortest distance of the plane from the origin is :

1 \(\sqrt{\frac{3}{109}}\)
2 \(\sqrt{\frac{5}{142}}\)
3 \(\sqrt{\frac{5}{71}}\)
4 \(\sqrt{\frac{1}{142}}\)
JEE Main-29.06.2022
Three Dimensional Geometry

121227 The shortest distance between the lines \(\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}\) and \(\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}\) is

1 \(2 \sqrt{3}\)
2 \(5 \sqrt{3}\)
3 \(4 \sqrt{3}\)
4 \(3 \sqrt{3}\)
JEE Main-29.01.2023
Three Dimensional Geometry

121229 Let the plane \(P: 8 x+\alpha_1 y+\alpha_2 z+12=0\) be parallel to the line \(\frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{5}\). If the intercept of \(P\) on the \(y\)-axis is 1 , then the distance between \(P\) and \(L\) is

1 \(\sqrt{\frac{2}{7}}\)
2 \(\frac{6}{\sqrt{14}}\)
3 \(\sqrt{\frac{7}{2}}\)
4 \(\sqrt{14}\)
JEE Main-31.01.2023
Three Dimensional Geometry

121230 The shortest distance between the lines \(\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}\) and \(\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0}\) is

1 6
2 9
3 7
4 8
JEE Main-10.04.2023
Join With Us for More Updates
Three Dimensional Geometry

121226 Let \(\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z+3}{-1}\) lie on the plane \(p x-q y\) \(+z=5\), for some \(p, q \in R\). The shortest distance of the plane from the origin is :

1 \(\sqrt{\frac{3}{109}}\)
2 \(\sqrt{\frac{5}{142}}\)
3 \(\sqrt{\frac{5}{71}}\)
4 \(\sqrt{\frac{1}{142}}\)
JEE Main-29.06.2022
Three Dimensional Geometry

121227 The shortest distance between the lines \(\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}\) and \(\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}\) is

1 \(2 \sqrt{3}\)
2 \(5 \sqrt{3}\)
3 \(4 \sqrt{3}\)
4 \(3 \sqrt{3}\)
JEE Main-29.01.2023
Three Dimensional Geometry

121229 Let the plane \(P: 8 x+\alpha_1 y+\alpha_2 z+12=0\) be parallel to the line \(\frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{5}\). If the intercept of \(P\) on the \(y\)-axis is 1 , then the distance between \(P\) and \(L\) is

1 \(\sqrt{\frac{2}{7}}\)
2 \(\frac{6}{\sqrt{14}}\)
3 \(\sqrt{\frac{7}{2}}\)
4 \(\sqrt{14}\)
JEE Main-31.01.2023
Three Dimensional Geometry

121230 The shortest distance between the lines \(\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}\) and \(\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0}\) is

1 6
2 9
3 7
4 8
JEE Main-10.04.2023
For More Updates join with Us
Three Dimensional Geometry

121226 Let \(\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z+3}{-1}\) lie on the plane \(p x-q y\) \(+z=5\), for some \(p, q \in R\). The shortest distance of the plane from the origin is :

1 \(\sqrt{\frac{3}{109}}\)
2 \(\sqrt{\frac{5}{142}}\)
3 \(\sqrt{\frac{5}{71}}\)
4 \(\sqrt{\frac{1}{142}}\)
JEE Main-29.06.2022
Three Dimensional Geometry

121227 The shortest distance between the lines \(\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}\) and \(\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}\) is

1 \(2 \sqrt{3}\)
2 \(5 \sqrt{3}\)
3 \(4 \sqrt{3}\)
4 \(3 \sqrt{3}\)
JEE Main-29.01.2023
Three Dimensional Geometry

121229 Let the plane \(P: 8 x+\alpha_1 y+\alpha_2 z+12=0\) be parallel to the line \(\frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{5}\). If the intercept of \(P\) on the \(y\)-axis is 1 , then the distance between \(P\) and \(L\) is

1 \(\sqrt{\frac{2}{7}}\)
2 \(\frac{6}{\sqrt{14}}\)
3 \(\sqrt{\frac{7}{2}}\)
4 \(\sqrt{14}\)
JEE Main-31.01.2023
Three Dimensional Geometry

121230 The shortest distance between the lines \(\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}\) and \(\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0}\) is

1 6
2 9
3 7
4 8
JEE Main-10.04.2023
NEET DIGITAL LIBRARY