Distance and Image of a Point from a Plane
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Three Dimensional Geometry

121338 The image of the point \((1,6,3)\) in the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\) is

1 \((1,0,7)\)
2 \((7,0,1)\)
3 \((2,7,0)\)
4 \((-1,-6,-3)\)
Karnataka CET-2018
Three Dimensional Geometry

121339 The distance of the point \((1,-5,9)\) from the plane \(x+y+z=5\) measured along a straight line \(x=y=z\) is \(2 \sqrt{3} k\) then the value of \(k\) is

1 5
2 6
3 \(\sqrt{3}\)
4 4
BITSAT-2017
Three Dimensional Geometry

121341 If a line makes an angle of \(\frac{\pi}{3}\) with each of \(x\) and \(y\)-axis, then the acute angle made by \(z\)-axis is

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{3}\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Karnataka CET-2020
Three Dimensional Geometry

121342 Acute angle between the line
\(\frac{x-5}{2}=\frac{y+1}{-1}=\frac{z+4}{1}\) and
the
plane \(3 x-4 y-z+5=0\) is

1 \(\cos ^{-1}\left(\frac{9}{\sqrt{364}}\right)\)
2 \(\cos ^{-1}\left(\frac{5}{2 \sqrt{13}}\right)\)
3 \(\sin ^{-1}\left(\frac{9}{\sqrt{364}}\right)\)
4 \(\sin ^{-1}\left(\frac{5}{2 \sqrt{13}}\right)\)
Karnataka CET-2019
Three Dimensional Geometry

121343 The angle between the lines \(2 x=3 y=-z\) and \(6 x=-y=-4 z\) is

1 \(0^{\circ}\)
2 \(45^{\circ}\)
3 \(90^{\circ}\)
4 \(30^{\circ}\)
Karnataka CET-2018
NEET DIGITAL LIBRARY
Three Dimensional Geometry

121338 The image of the point \((1,6,3)\) in the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\) is

1 \((1,0,7)\)
2 \((7,0,1)\)
3 \((2,7,0)\)
4 \((-1,-6,-3)\)
Karnataka CET-2018
Three Dimensional Geometry

121339 The distance of the point \((1,-5,9)\) from the plane \(x+y+z=5\) measured along a straight line \(x=y=z\) is \(2 \sqrt{3} k\) then the value of \(k\) is

1 5
2 6
3 \(\sqrt{3}\)
4 4
BITSAT-2017
Three Dimensional Geometry

121341 If a line makes an angle of \(\frac{\pi}{3}\) with each of \(x\) and \(y\)-axis, then the acute angle made by \(z\)-axis is

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{3}\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Karnataka CET-2020
Three Dimensional Geometry

121342 Acute angle between the line
\(\frac{x-5}{2}=\frac{y+1}{-1}=\frac{z+4}{1}\) and
the
plane \(3 x-4 y-z+5=0\) is

1 \(\cos ^{-1}\left(\frac{9}{\sqrt{364}}\right)\)
2 \(\cos ^{-1}\left(\frac{5}{2 \sqrt{13}}\right)\)
3 \(\sin ^{-1}\left(\frac{9}{\sqrt{364}}\right)\)
4 \(\sin ^{-1}\left(\frac{5}{2 \sqrt{13}}\right)\)
Karnataka CET-2019
Three Dimensional Geometry

121343 The angle between the lines \(2 x=3 y=-z\) and \(6 x=-y=-4 z\) is

1 \(0^{\circ}\)
2 \(45^{\circ}\)
3 \(90^{\circ}\)
4 \(30^{\circ}\)
Karnataka CET-2018
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Three Dimensional Geometry

121338 The image of the point \((1,6,3)\) in the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\) is

1 \((1,0,7)\)
2 \((7,0,1)\)
3 \((2,7,0)\)
4 \((-1,-6,-3)\)
Karnataka CET-2018
Three Dimensional Geometry

121339 The distance of the point \((1,-5,9)\) from the plane \(x+y+z=5\) measured along a straight line \(x=y=z\) is \(2 \sqrt{3} k\) then the value of \(k\) is

1 5
2 6
3 \(\sqrt{3}\)
4 4
BITSAT-2017
Three Dimensional Geometry

121341 If a line makes an angle of \(\frac{\pi}{3}\) with each of \(x\) and \(y\)-axis, then the acute angle made by \(z\)-axis is

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{3}\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Karnataka CET-2020
Three Dimensional Geometry

121342 Acute angle between the line
\(\frac{x-5}{2}=\frac{y+1}{-1}=\frac{z+4}{1}\) and
the
plane \(3 x-4 y-z+5=0\) is

1 \(\cos ^{-1}\left(\frac{9}{\sqrt{364}}\right)\)
2 \(\cos ^{-1}\left(\frac{5}{2 \sqrt{13}}\right)\)
3 \(\sin ^{-1}\left(\frac{9}{\sqrt{364}}\right)\)
4 \(\sin ^{-1}\left(\frac{5}{2 \sqrt{13}}\right)\)
Karnataka CET-2019
Three Dimensional Geometry

121343 The angle between the lines \(2 x=3 y=-z\) and \(6 x=-y=-4 z\) is

1 \(0^{\circ}\)
2 \(45^{\circ}\)
3 \(90^{\circ}\)
4 \(30^{\circ}\)
Karnataka CET-2018
For More Updates join with Us
Three Dimensional Geometry

121338 The image of the point \((1,6,3)\) in the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\) is

1 \((1,0,7)\)
2 \((7,0,1)\)
3 \((2,7,0)\)
4 \((-1,-6,-3)\)
Karnataka CET-2018
Three Dimensional Geometry

121339 The distance of the point \((1,-5,9)\) from the plane \(x+y+z=5\) measured along a straight line \(x=y=z\) is \(2 \sqrt{3} k\) then the value of \(k\) is

1 5
2 6
3 \(\sqrt{3}\)
4 4
BITSAT-2017
Three Dimensional Geometry

121341 If a line makes an angle of \(\frac{\pi}{3}\) with each of \(x\) and \(y\)-axis, then the acute angle made by \(z\)-axis is

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{3}\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Karnataka CET-2020
Three Dimensional Geometry

121342 Acute angle between the line
\(\frac{x-5}{2}=\frac{y+1}{-1}=\frac{z+4}{1}\) and
the
plane \(3 x-4 y-z+5=0\) is

1 \(\cos ^{-1}\left(\frac{9}{\sqrt{364}}\right)\)
2 \(\cos ^{-1}\left(\frac{5}{2 \sqrt{13}}\right)\)
3 \(\sin ^{-1}\left(\frac{9}{\sqrt{364}}\right)\)
4 \(\sin ^{-1}\left(\frac{5}{2 \sqrt{13}}\right)\)
Karnataka CET-2019
Three Dimensional Geometry

121343 The angle between the lines \(2 x=3 y=-z\) and \(6 x=-y=-4 z\) is

1 \(0^{\circ}\)
2 \(45^{\circ}\)
3 \(90^{\circ}\)
4 \(30^{\circ}\)
Karnataka CET-2018
NEET DIGITAL LIBRARY
Three Dimensional Geometry

121338 The image of the point \((1,6,3)\) in the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\) is

1 \((1,0,7)\)
2 \((7,0,1)\)
3 \((2,7,0)\)
4 \((-1,-6,-3)\)
Karnataka CET-2018
Three Dimensional Geometry

121339 The distance of the point \((1,-5,9)\) from the plane \(x+y+z=5\) measured along a straight line \(x=y=z\) is \(2 \sqrt{3} k\) then the value of \(k\) is

1 5
2 6
3 \(\sqrt{3}\)
4 4
BITSAT-2017
Three Dimensional Geometry

121341 If a line makes an angle of \(\frac{\pi}{3}\) with each of \(x\) and \(y\)-axis, then the acute angle made by \(z\)-axis is

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{3}\)
3 \(\frac{\pi}{2}\)
4 \(\frac{\pi}{4}\)
Karnataka CET-2020
Three Dimensional Geometry

121342 Acute angle between the line
\(\frac{x-5}{2}=\frac{y+1}{-1}=\frac{z+4}{1}\) and
the
plane \(3 x-4 y-z+5=0\) is

1 \(\cos ^{-1}\left(\frac{9}{\sqrt{364}}\right)\)
2 \(\cos ^{-1}\left(\frac{5}{2 \sqrt{13}}\right)\)
3 \(\sin ^{-1}\left(\frac{9}{\sqrt{364}}\right)\)
4 \(\sin ^{-1}\left(\frac{5}{2 \sqrt{13}}\right)\)
Karnataka CET-2019
Three Dimensional Geometry

121343 The angle between the lines \(2 x=3 y=-z\) and \(6 x=-y=-4 z\) is

1 \(0^{\circ}\)
2 \(45^{\circ}\)
3 \(90^{\circ}\)
4 \(30^{\circ}\)
Karnataka CET-2018