Direction Angle, Direction Ratios and Direction Cosine
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Three Dimensional Geometry

121130 Direction ratios of the line which is perpendicular to the lines with direction ratios \(-1,2,2\) and \(0,2,1\) are

1 \(1,1,2\)
2 \(2,-1,2\)
3 \(-2,1,2\)
4 \(2,1,-2\)
MHT CET-2016
Three Dimensional Geometry

121131 Direction cosines of the line \(\frac{x+2}{2}=\frac{2 y-5}{3}, z=-1\) are

1 \(\frac{4}{5}, \frac{3}{5}, 0\)
2 \(\frac{3}{5}, \frac{4}{5}, \frac{1}{5}\)
3 \(-\frac{3}{5}, \frac{4}{5}, 0\)
4 \(\frac{4}{5},-\frac{2}{5}, \frac{1}{5}\)
MHT CET-2016
Three Dimensional Geometry

121133 A plane meets the axes in \(A, B\) and \(C\) such that centroid of the \(\triangle \mathrm{ABC}\) is \((1,2,3)\). The equation of the plane is

1 \(x+\frac{y}{2}+\frac{z}{3}=1\)
2 \(\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1\)
3 \(x+2 y+3 z=1\)
4 None of these
MHT CET-2011
Three Dimensional Geometry

121135 The cosine of the angle \(A\) of the triangle with vertices \(A(1,-1,2), B(6,11,2), C(1,2,6)\) is

1 \(\frac{63}{65}\)
2 \(\frac{36}{65}\)
3 \(\frac{16}{65}\)
4 none of these
COMEDK-2019
Three Dimensional Geometry

121136 If the angle between the vectors \(\vec{a}\) and \(\vec{b}\) having direction ratios \(1,2,1\) and \(1,3 \mathrm{k}, 1\) is \(\frac{\pi}{4}\),thenk \(=\)

1 \(\frac{2 \pm 3 \sqrt{2}}{3}\)
2 \(\frac{-2 \pm 3 \sqrt{2}}{3}\)
3 \(\frac{4 \pm 3 \sqrt{2}}{3}\)
4 \(\frac{-4 \pm 3 \sqrt{2}}{3}\)
COMEDK-2020
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Three Dimensional Geometry

121130 Direction ratios of the line which is perpendicular to the lines with direction ratios \(-1,2,2\) and \(0,2,1\) are

1 \(1,1,2\)
2 \(2,-1,2\)
3 \(-2,1,2\)
4 \(2,1,-2\)
MHT CET-2016
Three Dimensional Geometry

121131 Direction cosines of the line \(\frac{x+2}{2}=\frac{2 y-5}{3}, z=-1\) are

1 \(\frac{4}{5}, \frac{3}{5}, 0\)
2 \(\frac{3}{5}, \frac{4}{5}, \frac{1}{5}\)
3 \(-\frac{3}{5}, \frac{4}{5}, 0\)
4 \(\frac{4}{5},-\frac{2}{5}, \frac{1}{5}\)
MHT CET-2016
Three Dimensional Geometry

121133 A plane meets the axes in \(A, B\) and \(C\) such that centroid of the \(\triangle \mathrm{ABC}\) is \((1,2,3)\). The equation of the plane is

1 \(x+\frac{y}{2}+\frac{z}{3}=1\)
2 \(\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1\)
3 \(x+2 y+3 z=1\)
4 None of these
MHT CET-2011
Three Dimensional Geometry

121135 The cosine of the angle \(A\) of the triangle with vertices \(A(1,-1,2), B(6,11,2), C(1,2,6)\) is

1 \(\frac{63}{65}\)
2 \(\frac{36}{65}\)
3 \(\frac{16}{65}\)
4 none of these
COMEDK-2019
Three Dimensional Geometry

121136 If the angle between the vectors \(\vec{a}\) and \(\vec{b}\) having direction ratios \(1,2,1\) and \(1,3 \mathrm{k}, 1\) is \(\frac{\pi}{4}\),thenk \(=\)

1 \(\frac{2 \pm 3 \sqrt{2}}{3}\)
2 \(\frac{-2 \pm 3 \sqrt{2}}{3}\)
3 \(\frac{4 \pm 3 \sqrt{2}}{3}\)
4 \(\frac{-4 \pm 3 \sqrt{2}}{3}\)
COMEDK-2020
For More Updates join with Us
Three Dimensional Geometry

121130 Direction ratios of the line which is perpendicular to the lines with direction ratios \(-1,2,2\) and \(0,2,1\) are

1 \(1,1,2\)
2 \(2,-1,2\)
3 \(-2,1,2\)
4 \(2,1,-2\)
MHT CET-2016
Three Dimensional Geometry

121131 Direction cosines of the line \(\frac{x+2}{2}=\frac{2 y-5}{3}, z=-1\) are

1 \(\frac{4}{5}, \frac{3}{5}, 0\)
2 \(\frac{3}{5}, \frac{4}{5}, \frac{1}{5}\)
3 \(-\frac{3}{5}, \frac{4}{5}, 0\)
4 \(\frac{4}{5},-\frac{2}{5}, \frac{1}{5}\)
MHT CET-2016
Three Dimensional Geometry

121133 A plane meets the axes in \(A, B\) and \(C\) such that centroid of the \(\triangle \mathrm{ABC}\) is \((1,2,3)\). The equation of the plane is

1 \(x+\frac{y}{2}+\frac{z}{3}=1\)
2 \(\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1\)
3 \(x+2 y+3 z=1\)
4 None of these
MHT CET-2011
Three Dimensional Geometry

121135 The cosine of the angle \(A\) of the triangle with vertices \(A(1,-1,2), B(6,11,2), C(1,2,6)\) is

1 \(\frac{63}{65}\)
2 \(\frac{36}{65}\)
3 \(\frac{16}{65}\)
4 none of these
COMEDK-2019
Three Dimensional Geometry

121136 If the angle between the vectors \(\vec{a}\) and \(\vec{b}\) having direction ratios \(1,2,1\) and \(1,3 \mathrm{k}, 1\) is \(\frac{\pi}{4}\),thenk \(=\)

1 \(\frac{2 \pm 3 \sqrt{2}}{3}\)
2 \(\frac{-2 \pm 3 \sqrt{2}}{3}\)
3 \(\frac{4 \pm 3 \sqrt{2}}{3}\)
4 \(\frac{-4 \pm 3 \sqrt{2}}{3}\)
COMEDK-2020
NEET DIGITAL LIBRARY
Three Dimensional Geometry

121130 Direction ratios of the line which is perpendicular to the lines with direction ratios \(-1,2,2\) and \(0,2,1\) are

1 \(1,1,2\)
2 \(2,-1,2\)
3 \(-2,1,2\)
4 \(2,1,-2\)
MHT CET-2016
Three Dimensional Geometry

121131 Direction cosines of the line \(\frac{x+2}{2}=\frac{2 y-5}{3}, z=-1\) are

1 \(\frac{4}{5}, \frac{3}{5}, 0\)
2 \(\frac{3}{5}, \frac{4}{5}, \frac{1}{5}\)
3 \(-\frac{3}{5}, \frac{4}{5}, 0\)
4 \(\frac{4}{5},-\frac{2}{5}, \frac{1}{5}\)
MHT CET-2016
Three Dimensional Geometry

121133 A plane meets the axes in \(A, B\) and \(C\) such that centroid of the \(\triangle \mathrm{ABC}\) is \((1,2,3)\). The equation of the plane is

1 \(x+\frac{y}{2}+\frac{z}{3}=1\)
2 \(\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1\)
3 \(x+2 y+3 z=1\)
4 None of these
MHT CET-2011
Three Dimensional Geometry

121135 The cosine of the angle \(A\) of the triangle with vertices \(A(1,-1,2), B(6,11,2), C(1,2,6)\) is

1 \(\frac{63}{65}\)
2 \(\frac{36}{65}\)
3 \(\frac{16}{65}\)
4 none of these
COMEDK-2019
Three Dimensional Geometry

121136 If the angle between the vectors \(\vec{a}\) and \(\vec{b}\) having direction ratios \(1,2,1\) and \(1,3 \mathrm{k}, 1\) is \(\frac{\pi}{4}\),thenk \(=\)

1 \(\frac{2 \pm 3 \sqrt{2}}{3}\)
2 \(\frac{-2 \pm 3 \sqrt{2}}{3}\)
3 \(\frac{4 \pm 3 \sqrt{2}}{3}\)
4 \(\frac{-4 \pm 3 \sqrt{2}}{3}\)
COMEDK-2020
Join With Us for More Updates
Three Dimensional Geometry

121130 Direction ratios of the line which is perpendicular to the lines with direction ratios \(-1,2,2\) and \(0,2,1\) are

1 \(1,1,2\)
2 \(2,-1,2\)
3 \(-2,1,2\)
4 \(2,1,-2\)
MHT CET-2016
Three Dimensional Geometry

121131 Direction cosines of the line \(\frac{x+2}{2}=\frac{2 y-5}{3}, z=-1\) are

1 \(\frac{4}{5}, \frac{3}{5}, 0\)
2 \(\frac{3}{5}, \frac{4}{5}, \frac{1}{5}\)
3 \(-\frac{3}{5}, \frac{4}{5}, 0\)
4 \(\frac{4}{5},-\frac{2}{5}, \frac{1}{5}\)
MHT CET-2016
Three Dimensional Geometry

121133 A plane meets the axes in \(A, B\) and \(C\) such that centroid of the \(\triangle \mathrm{ABC}\) is \((1,2,3)\). The equation of the plane is

1 \(x+\frac{y}{2}+\frac{z}{3}=1\)
2 \(\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1\)
3 \(x+2 y+3 z=1\)
4 None of these
MHT CET-2011
Three Dimensional Geometry

121135 The cosine of the angle \(A\) of the triangle with vertices \(A(1,-1,2), B(6,11,2), C(1,2,6)\) is

1 \(\frac{63}{65}\)
2 \(\frac{36}{65}\)
3 \(\frac{16}{65}\)
4 none of these
COMEDK-2019
Three Dimensional Geometry

121136 If the angle between the vectors \(\vec{a}\) and \(\vec{b}\) having direction ratios \(1,2,1\) and \(1,3 \mathrm{k}, 1\) is \(\frac{\pi}{4}\),thenk \(=\)

1 \(\frac{2 \pm 3 \sqrt{2}}{3}\)
2 \(\frac{-2 \pm 3 \sqrt{2}}{3}\)
3 \(\frac{4 \pm 3 \sqrt{2}}{3}\)
4 \(\frac{-4 \pm 3 \sqrt{2}}{3}\)
COMEDK-2020