Direction Angle, Direction Ratios and Direction Cosine
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Three Dimensional Geometry

121159 What is the sum of squares of direction cosines of all the four diagonals of the cube?

1 1
2 2
3 4
4 Cannot be determined as the data is inadequate
SCRA-2014
Three Dimensional Geometry

121160 \(\quad A(2,3,5), B(\alpha, 3,3)\) and \(C(7,5, \beta)\) are the vertices of triangle. If the median trough \(A\) is equally inclined with the co-ordinate axes, then \(\cos ^{-1}\left(\frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}}\right)=\)

1 \(\cos ^{-1}\left(\frac{-1}{9}\right)\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{3}\)
4 \(\cos ^{-1}\left(\frac{2}{5}\right)\)
AP EAMCET-20.04.2019
Three Dimensional Geometry

121161 If a line makes angles \(\frac{\pi}{4}\) and \(\frac{\pi}{3}\) with \(Y\)-axis and \(\mathrm{Z}\)-axis respectively, then the obtuse angle made by that line with \(\mathrm{X}\)-axis is

1 \(\frac{\pi}{3}\)
2 \(\frac{2 \pi}{3}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{5 \pi}{6}\)
AP EAMCET-24.04.2018
Three Dimensional Geometry

121162 The direction ratio of the two lines \(A B\) and \(A C\) are \(1,-1,-1\), and \(2,-1,1\). The direction ratio of the normal to the plane \(\mathrm{ABC}\) are

1 2, 3, - 1
2 2, 2, 1
3 \(3,2,-1\)
4 \(-1,2,3\)
AP EAMCET-2013
For More Updates join with Us
Three Dimensional Geometry

121159 What is the sum of squares of direction cosines of all the four diagonals of the cube?

1 1
2 2
3 4
4 Cannot be determined as the data is inadequate
SCRA-2014
Three Dimensional Geometry

121160 \(\quad A(2,3,5), B(\alpha, 3,3)\) and \(C(7,5, \beta)\) are the vertices of triangle. If the median trough \(A\) is equally inclined with the co-ordinate axes, then \(\cos ^{-1}\left(\frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}}\right)=\)

1 \(\cos ^{-1}\left(\frac{-1}{9}\right)\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{3}\)
4 \(\cos ^{-1}\left(\frac{2}{5}\right)\)
AP EAMCET-20.04.2019
Three Dimensional Geometry

121161 If a line makes angles \(\frac{\pi}{4}\) and \(\frac{\pi}{3}\) with \(Y\)-axis and \(\mathrm{Z}\)-axis respectively, then the obtuse angle made by that line with \(\mathrm{X}\)-axis is

1 \(\frac{\pi}{3}\)
2 \(\frac{2 \pi}{3}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{5 \pi}{6}\)
AP EAMCET-24.04.2018
Three Dimensional Geometry

121162 The direction ratio of the two lines \(A B\) and \(A C\) are \(1,-1,-1\), and \(2,-1,1\). The direction ratio of the normal to the plane \(\mathrm{ABC}\) are

1 2, 3, - 1
2 2, 2, 1
3 \(3,2,-1\)
4 \(-1,2,3\)
AP EAMCET-2013
NEET DIGITAL LIBRARY
Three Dimensional Geometry

121159 What is the sum of squares of direction cosines of all the four diagonals of the cube?

1 1
2 2
3 4
4 Cannot be determined as the data is inadequate
SCRA-2014
Three Dimensional Geometry

121160 \(\quad A(2,3,5), B(\alpha, 3,3)\) and \(C(7,5, \beta)\) are the vertices of triangle. If the median trough \(A\) is equally inclined with the co-ordinate axes, then \(\cos ^{-1}\left(\frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}}\right)=\)

1 \(\cos ^{-1}\left(\frac{-1}{9}\right)\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{3}\)
4 \(\cos ^{-1}\left(\frac{2}{5}\right)\)
AP EAMCET-20.04.2019
Three Dimensional Geometry

121161 If a line makes angles \(\frac{\pi}{4}\) and \(\frac{\pi}{3}\) with \(Y\)-axis and \(\mathrm{Z}\)-axis respectively, then the obtuse angle made by that line with \(\mathrm{X}\)-axis is

1 \(\frac{\pi}{3}\)
2 \(\frac{2 \pi}{3}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{5 \pi}{6}\)
AP EAMCET-24.04.2018
Three Dimensional Geometry

121162 The direction ratio of the two lines \(A B\) and \(A C\) are \(1,-1,-1\), and \(2,-1,1\). The direction ratio of the normal to the plane \(\mathrm{ABC}\) are

1 2, 3, - 1
2 2, 2, 1
3 \(3,2,-1\)
4 \(-1,2,3\)
AP EAMCET-2013
Join With Us for More Updates
Three Dimensional Geometry

121159 What is the sum of squares of direction cosines of all the four diagonals of the cube?

1 1
2 2
3 4
4 Cannot be determined as the data is inadequate
SCRA-2014
Three Dimensional Geometry

121160 \(\quad A(2,3,5), B(\alpha, 3,3)\) and \(C(7,5, \beta)\) are the vertices of triangle. If the median trough \(A\) is equally inclined with the co-ordinate axes, then \(\cos ^{-1}\left(\frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}}\right)=\)

1 \(\cos ^{-1}\left(\frac{-1}{9}\right)\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{3}\)
4 \(\cos ^{-1}\left(\frac{2}{5}\right)\)
AP EAMCET-20.04.2019
Three Dimensional Geometry

121161 If a line makes angles \(\frac{\pi}{4}\) and \(\frac{\pi}{3}\) with \(Y\)-axis and \(\mathrm{Z}\)-axis respectively, then the obtuse angle made by that line with \(\mathrm{X}\)-axis is

1 \(\frac{\pi}{3}\)
2 \(\frac{2 \pi}{3}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{5 \pi}{6}\)
AP EAMCET-24.04.2018
Three Dimensional Geometry

121162 The direction ratio of the two lines \(A B\) and \(A C\) are \(1,-1,-1\), and \(2,-1,1\). The direction ratio of the normal to the plane \(\mathrm{ABC}\) are

1 2, 3, - 1
2 2, 2, 1
3 \(3,2,-1\)
4 \(-1,2,3\)
AP EAMCET-2013
For More Updates join with Us