Angle Between Two Lines, Two Planes, a Line and a Plane
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Three Dimensional Geometry

121323 The angle between the lines whose direction cosines are \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)\) and \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)\) is

1 \(\pi\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{4}\)
Karnataka CET-2021
Three Dimensional Geometry

121324 The angle between the lines \(\frac{x-2}{3}=\frac{y+1}{-2}, z=2\) and \(\frac{x-1}{1}=\frac{y+3}{3}=\frac{z+5}{2}\)

1 \(\cos ^{-1}\left(\frac{-3}{\sqrt{182}}\right)\)
2 \(\cos ^{-1}\left(\frac{5}{\sqrt{182}}\right)\)
3 \(\cos ^{-1}\left(\frac{3}{\sqrt{182}}\right)\)
4 \(\cos ^{-1}\left(\frac{-5}{\sqrt{182}}\right)\)
CG PET- 2011
Three Dimensional Geometry

121325 The angle between the lines
\(\frac{x-2}{3}=\frac{y+1}{-2} ; z=2\)
and \(\frac{x-1}{1}=\frac{2 y+3}{3} ; \frac{z+5}{2}\) is

1 \(\frac{\pi}{3}\)
2 \(\frac{\pi}{6}\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
CG PET- 2013
Three Dimensional Geometry

121326 The angle between planes \(2 x-y+z=6\) and \(x+\) \(y+2 z=3\) is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(\cos ^{-1} \sqrt{\frac{3}{2}}\)
4 \(\sin ^{-1} \sqrt{\frac{3}{2}}\)
CG PET- 2014
NEET DIGITAL LIBRARY
Three Dimensional Geometry

121323 The angle between the lines whose direction cosines are \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)\) and \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)\) is

1 \(\pi\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{4}\)
Karnataka CET-2021
Three Dimensional Geometry

121324 The angle between the lines \(\frac{x-2}{3}=\frac{y+1}{-2}, z=2\) and \(\frac{x-1}{1}=\frac{y+3}{3}=\frac{z+5}{2}\)

1 \(\cos ^{-1}\left(\frac{-3}{\sqrt{182}}\right)\)
2 \(\cos ^{-1}\left(\frac{5}{\sqrt{182}}\right)\)
3 \(\cos ^{-1}\left(\frac{3}{\sqrt{182}}\right)\)
4 \(\cos ^{-1}\left(\frac{-5}{\sqrt{182}}\right)\)
CG PET- 2011
Three Dimensional Geometry

121325 The angle between the lines
\(\frac{x-2}{3}=\frac{y+1}{-2} ; z=2\)
and \(\frac{x-1}{1}=\frac{2 y+3}{3} ; \frac{z+5}{2}\) is

1 \(\frac{\pi}{3}\)
2 \(\frac{\pi}{6}\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
CG PET- 2013
Three Dimensional Geometry

121326 The angle between planes \(2 x-y+z=6\) and \(x+\) \(y+2 z=3\) is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(\cos ^{-1} \sqrt{\frac{3}{2}}\)
4 \(\sin ^{-1} \sqrt{\frac{3}{2}}\)
CG PET- 2014
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Three Dimensional Geometry

121323 The angle between the lines whose direction cosines are \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)\) and \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)\) is

1 \(\pi\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{4}\)
Karnataka CET-2021
Three Dimensional Geometry

121324 The angle between the lines \(\frac{x-2}{3}=\frac{y+1}{-2}, z=2\) and \(\frac{x-1}{1}=\frac{y+3}{3}=\frac{z+5}{2}\)

1 \(\cos ^{-1}\left(\frac{-3}{\sqrt{182}}\right)\)
2 \(\cos ^{-1}\left(\frac{5}{\sqrt{182}}\right)\)
3 \(\cos ^{-1}\left(\frac{3}{\sqrt{182}}\right)\)
4 \(\cos ^{-1}\left(\frac{-5}{\sqrt{182}}\right)\)
CG PET- 2011
Three Dimensional Geometry

121325 The angle between the lines
\(\frac{x-2}{3}=\frac{y+1}{-2} ; z=2\)
and \(\frac{x-1}{1}=\frac{2 y+3}{3} ; \frac{z+5}{2}\) is

1 \(\frac{\pi}{3}\)
2 \(\frac{\pi}{6}\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
CG PET- 2013
Three Dimensional Geometry

121326 The angle between planes \(2 x-y+z=6\) and \(x+\) \(y+2 z=3\) is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(\cos ^{-1} \sqrt{\frac{3}{2}}\)
4 \(\sin ^{-1} \sqrt{\frac{3}{2}}\)
CG PET- 2014
For More Updates join with Us
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Three Dimensional Geometry

121323 The angle between the lines whose direction cosines are \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)\) and \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)\) is

1 \(\pi\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{4}\)
Karnataka CET-2021
Three Dimensional Geometry

121324 The angle between the lines \(\frac{x-2}{3}=\frac{y+1}{-2}, z=2\) and \(\frac{x-1}{1}=\frac{y+3}{3}=\frac{z+5}{2}\)

1 \(\cos ^{-1}\left(\frac{-3}{\sqrt{182}}\right)\)
2 \(\cos ^{-1}\left(\frac{5}{\sqrt{182}}\right)\)
3 \(\cos ^{-1}\left(\frac{3}{\sqrt{182}}\right)\)
4 \(\cos ^{-1}\left(\frac{-5}{\sqrt{182}}\right)\)
CG PET- 2011
Three Dimensional Geometry

121325 The angle between the lines
\(\frac{x-2}{3}=\frac{y+1}{-2} ; z=2\)
and \(\frac{x-1}{1}=\frac{2 y+3}{3} ; \frac{z+5}{2}\) is

1 \(\frac{\pi}{3}\)
2 \(\frac{\pi}{6}\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
CG PET- 2013
Three Dimensional Geometry

121326 The angle between planes \(2 x-y+z=6\) and \(x+\) \(y+2 z=3\) is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(\cos ^{-1} \sqrt{\frac{3}{2}}\)
4 \(\sin ^{-1} \sqrt{\frac{3}{2}}\)
CG PET- 2014
NEET DIGITAL LIBRARY