Direction Angle, Direction Ratios and Direction Cosine
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Three Dimensional Geometry

121113 XY-plane divides the line joining the points \(A(2,3,-5)\) and \(B(-1,-2,-3)\) in the ratio

1 \(2: 1\) internally
2 \(5: 3\) internally
3 \(3: 2\) externally
4 \(5: 3\) externally
Karnataka CET-2019
Three Dimensional Geometry

121114 A vector \(\overline{\mathbf{v}}\) is equally inclined to the \(\mathbf{X}\)-axis, \(\mathbf{Y}\)-axis and \(\mathrm{Z}\)-axis respectively, its direction cosines are

1 \(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\)
2 \(-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\)
3 \(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\) or \(-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\)
4 None of these
MHT CET-2011
Three Dimensional Geometry

121115 What is the value of \(n\) so that the angle between the lines having direction ratios \((1,1,1)\) and \((1\), \(-1, n)\) is \(60^{\circ}\) ?

1 \(\sqrt{3}\)
2 \(\sqrt{6}\)
3 3
4 None of these
BITSAT-2012
Three Dimensional Geometry

121116 The projection of line joining \((3,4,5)\) and \((4,6\), \(3)\) on the line joining \((-1,2,4)\) and \((1,0,5)\) is

1 \(\frac{4}{3}\)
2 \(\frac{2}{3}\)
3 \(\frac{8}{3}\)
4 \(\frac{1}{3}\)
BITSAT-2018
Three Dimensional Geometry

121117 The ratio in which the line joining \((2,1,5)\) and \((3,4,3)\) is divided by the plane \((x+y-z)=\frac{1}{2}\) is :

1 \(3: 5\)
2 \(5: 7\)
3 \(1: 3\)
4 \(4: 5\)
BITSAT-2017
NEET DIGITAL LIBRARY
Three Dimensional Geometry

121113 XY-plane divides the line joining the points \(A(2,3,-5)\) and \(B(-1,-2,-3)\) in the ratio

1 \(2: 1\) internally
2 \(5: 3\) internally
3 \(3: 2\) externally
4 \(5: 3\) externally
Karnataka CET-2019
Three Dimensional Geometry

121114 A vector \(\overline{\mathbf{v}}\) is equally inclined to the \(\mathbf{X}\)-axis, \(\mathbf{Y}\)-axis and \(\mathrm{Z}\)-axis respectively, its direction cosines are

1 \(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\)
2 \(-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\)
3 \(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\) or \(-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\)
4 None of these
MHT CET-2011
Three Dimensional Geometry

121115 What is the value of \(n\) so that the angle between the lines having direction ratios \((1,1,1)\) and \((1\), \(-1, n)\) is \(60^{\circ}\) ?

1 \(\sqrt{3}\)
2 \(\sqrt{6}\)
3 3
4 None of these
BITSAT-2012
Three Dimensional Geometry

121116 The projection of line joining \((3,4,5)\) and \((4,6\), \(3)\) on the line joining \((-1,2,4)\) and \((1,0,5)\) is

1 \(\frac{4}{3}\)
2 \(\frac{2}{3}\)
3 \(\frac{8}{3}\)
4 \(\frac{1}{3}\)
BITSAT-2018
Three Dimensional Geometry

121117 The ratio in which the line joining \((2,1,5)\) and \((3,4,3)\) is divided by the plane \((x+y-z)=\frac{1}{2}\) is :

1 \(3: 5\)
2 \(5: 7\)
3 \(1: 3\)
4 \(4: 5\)
BITSAT-2017
Join With Us for More Updates
Three Dimensional Geometry

121113 XY-plane divides the line joining the points \(A(2,3,-5)\) and \(B(-1,-2,-3)\) in the ratio

1 \(2: 1\) internally
2 \(5: 3\) internally
3 \(3: 2\) externally
4 \(5: 3\) externally
Karnataka CET-2019
Three Dimensional Geometry

121114 A vector \(\overline{\mathbf{v}}\) is equally inclined to the \(\mathbf{X}\)-axis, \(\mathbf{Y}\)-axis and \(\mathrm{Z}\)-axis respectively, its direction cosines are

1 \(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\)
2 \(-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\)
3 \(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\) or \(-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\)
4 None of these
MHT CET-2011
Three Dimensional Geometry

121115 What is the value of \(n\) so that the angle between the lines having direction ratios \((1,1,1)\) and \((1\), \(-1, n)\) is \(60^{\circ}\) ?

1 \(\sqrt{3}\)
2 \(\sqrt{6}\)
3 3
4 None of these
BITSAT-2012
Three Dimensional Geometry

121116 The projection of line joining \((3,4,5)\) and \((4,6\), \(3)\) on the line joining \((-1,2,4)\) and \((1,0,5)\) is

1 \(\frac{4}{3}\)
2 \(\frac{2}{3}\)
3 \(\frac{8}{3}\)
4 \(\frac{1}{3}\)
BITSAT-2018
Three Dimensional Geometry

121117 The ratio in which the line joining \((2,1,5)\) and \((3,4,3)\) is divided by the plane \((x+y-z)=\frac{1}{2}\) is :

1 \(3: 5\)
2 \(5: 7\)
3 \(1: 3\)
4 \(4: 5\)
BITSAT-2017
For More Updates join with Us
Three Dimensional Geometry

121113 XY-plane divides the line joining the points \(A(2,3,-5)\) and \(B(-1,-2,-3)\) in the ratio

1 \(2: 1\) internally
2 \(5: 3\) internally
3 \(3: 2\) externally
4 \(5: 3\) externally
Karnataka CET-2019
Three Dimensional Geometry

121114 A vector \(\overline{\mathbf{v}}\) is equally inclined to the \(\mathbf{X}\)-axis, \(\mathbf{Y}\)-axis and \(\mathrm{Z}\)-axis respectively, its direction cosines are

1 \(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\)
2 \(-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\)
3 \(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\) or \(-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\)
4 None of these
MHT CET-2011
Three Dimensional Geometry

121115 What is the value of \(n\) so that the angle between the lines having direction ratios \((1,1,1)\) and \((1\), \(-1, n)\) is \(60^{\circ}\) ?

1 \(\sqrt{3}\)
2 \(\sqrt{6}\)
3 3
4 None of these
BITSAT-2012
Three Dimensional Geometry

121116 The projection of line joining \((3,4,5)\) and \((4,6\), \(3)\) on the line joining \((-1,2,4)\) and \((1,0,5)\) is

1 \(\frac{4}{3}\)
2 \(\frac{2}{3}\)
3 \(\frac{8}{3}\)
4 \(\frac{1}{3}\)
BITSAT-2018
Three Dimensional Geometry

121117 The ratio in which the line joining \((2,1,5)\) and \((3,4,3)\) is divided by the plane \((x+y-z)=\frac{1}{2}\) is :

1 \(3: 5\)
2 \(5: 7\)
3 \(1: 3\)
4 \(4: 5\)
BITSAT-2017
NEET DIGITAL LIBRARY
Three Dimensional Geometry

121113 XY-plane divides the line joining the points \(A(2,3,-5)\) and \(B(-1,-2,-3)\) in the ratio

1 \(2: 1\) internally
2 \(5: 3\) internally
3 \(3: 2\) externally
4 \(5: 3\) externally
Karnataka CET-2019
Three Dimensional Geometry

121114 A vector \(\overline{\mathbf{v}}\) is equally inclined to the \(\mathbf{X}\)-axis, \(\mathbf{Y}\)-axis and \(\mathrm{Z}\)-axis respectively, its direction cosines are

1 \(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\)
2 \(-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\)
3 \(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\) or \(-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\)
4 None of these
MHT CET-2011
Three Dimensional Geometry

121115 What is the value of \(n\) so that the angle between the lines having direction ratios \((1,1,1)\) and \((1\), \(-1, n)\) is \(60^{\circ}\) ?

1 \(\sqrt{3}\)
2 \(\sqrt{6}\)
3 3
4 None of these
BITSAT-2012
Three Dimensional Geometry

121116 The projection of line joining \((3,4,5)\) and \((4,6\), \(3)\) on the line joining \((-1,2,4)\) and \((1,0,5)\) is

1 \(\frac{4}{3}\)
2 \(\frac{2}{3}\)
3 \(\frac{8}{3}\)
4 \(\frac{1}{3}\)
BITSAT-2018
Three Dimensional Geometry

121117 The ratio in which the line joining \((2,1,5)\) and \((3,4,3)\) is divided by the plane \((x+y-z)=\frac{1}{2}\) is :

1 \(3: 5\)
2 \(5: 7\)
3 \(1: 3\)
4 \(4: 5\)
BITSAT-2017