Direction Angle, Direction Ratios and Direction Cosine
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Three Dimensional Geometry

121176 The angle between a line with direction ratios \(2,2,1\) and the line joining the points \((3,1,4)\) and \((7,2,12\) )

1 \(\cos ^{-1}\left(\frac{2}{3}\right)\)
2 \(\cos ^{-1}\left(\frac{3}{4}\right)\)
3 \(\tan ^{-1}\left(\frac{-2}{3}\right)\)
4 \(\cos ^{-1}\left(\frac{1}{3}\right)\)
AP EAMCET-21.04.2019
Three Dimensional Geometry

121177 The angle between the lines whose direction cosines satisfy the equations \(l+\mathbf{m}+\mathbf{n}=\mathbf{0}\) and \(l^2\) \(+\mathbf{m}^2-\mathbf{n}^2=\mathbf{0}\) is

1 \(\frac{\pi}{2}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{3}\)
AP EAMCET-05.10.2021
Three Dimensional Geometry

121178 Assertion (A) The direction ratios of line \(L_1\) are \(2,5,7\) and those of line \(L_2\) are \(\frac{4}{\sqrt{19}}, \frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}\). The lines \(\mathrm{L}_1, \mathrm{~L}_2\) are parallel.
Reason (R) The direction ratios of a line \(L_1\) are \(a_1, b_1, c_1\) and those of another line \(L_2\) are \(a_2, b_2\), \(c_2\). The lines \(L_1\) and \(L_2\) are parallel if \(a_1 a_2+b_1 b_2\) \(+\mathbf{c}_1 \mathbf{c}_2=\mathbf{0}\)
The correct option among the following is

1 (A) is true, (R) is true and (R) is the correct explanation for (A).
2 (A) is true, (R) is true but (R) is not the correct explanation for (A).
3 (A) is true but (R) is false.
4 (A) is false but (R) is true.
TS EAMCET-11.09.2020
Three Dimensional Geometry

121180 If \(\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-7}{2}\) lies in the plane \(a x+b y\) \(+z=7\), then \(a+b=\)

1 -2
2 3
3 5
4 7
TS EAMCET-11.09.2020
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Three Dimensional Geometry

121176 The angle between a line with direction ratios \(2,2,1\) and the line joining the points \((3,1,4)\) and \((7,2,12\) )

1 \(\cos ^{-1}\left(\frac{2}{3}\right)\)
2 \(\cos ^{-1}\left(\frac{3}{4}\right)\)
3 \(\tan ^{-1}\left(\frac{-2}{3}\right)\)
4 \(\cos ^{-1}\left(\frac{1}{3}\right)\)
AP EAMCET-21.04.2019
Three Dimensional Geometry

121177 The angle between the lines whose direction cosines satisfy the equations \(l+\mathbf{m}+\mathbf{n}=\mathbf{0}\) and \(l^2\) \(+\mathbf{m}^2-\mathbf{n}^2=\mathbf{0}\) is

1 \(\frac{\pi}{2}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{3}\)
AP EAMCET-05.10.2021
Three Dimensional Geometry

121178 Assertion (A) The direction ratios of line \(L_1\) are \(2,5,7\) and those of line \(L_2\) are \(\frac{4}{\sqrt{19}}, \frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}\). The lines \(\mathrm{L}_1, \mathrm{~L}_2\) are parallel.
Reason (R) The direction ratios of a line \(L_1\) are \(a_1, b_1, c_1\) and those of another line \(L_2\) are \(a_2, b_2\), \(c_2\). The lines \(L_1\) and \(L_2\) are parallel if \(a_1 a_2+b_1 b_2\) \(+\mathbf{c}_1 \mathbf{c}_2=\mathbf{0}\)
The correct option among the following is

1 (A) is true, (R) is true and (R) is the correct explanation for (A).
2 (A) is true, (R) is true but (R) is not the correct explanation for (A).
3 (A) is true but (R) is false.
4 (A) is false but (R) is true.
TS EAMCET-11.09.2020
Three Dimensional Geometry

121180 If \(\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-7}{2}\) lies in the plane \(a x+b y\) \(+z=7\), then \(a+b=\)

1 -2
2 3
3 5
4 7
TS EAMCET-11.09.2020
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Three Dimensional Geometry

121176 The angle between a line with direction ratios \(2,2,1\) and the line joining the points \((3,1,4)\) and \((7,2,12\) )

1 \(\cos ^{-1}\left(\frac{2}{3}\right)\)
2 \(\cos ^{-1}\left(\frac{3}{4}\right)\)
3 \(\tan ^{-1}\left(\frac{-2}{3}\right)\)
4 \(\cos ^{-1}\left(\frac{1}{3}\right)\)
AP EAMCET-21.04.2019
Three Dimensional Geometry

121177 The angle between the lines whose direction cosines satisfy the equations \(l+\mathbf{m}+\mathbf{n}=\mathbf{0}\) and \(l^2\) \(+\mathbf{m}^2-\mathbf{n}^2=\mathbf{0}\) is

1 \(\frac{\pi}{2}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{3}\)
AP EAMCET-05.10.2021
Three Dimensional Geometry

121178 Assertion (A) The direction ratios of line \(L_1\) are \(2,5,7\) and those of line \(L_2\) are \(\frac{4}{\sqrt{19}}, \frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}\). The lines \(\mathrm{L}_1, \mathrm{~L}_2\) are parallel.
Reason (R) The direction ratios of a line \(L_1\) are \(a_1, b_1, c_1\) and those of another line \(L_2\) are \(a_2, b_2\), \(c_2\). The lines \(L_1\) and \(L_2\) are parallel if \(a_1 a_2+b_1 b_2\) \(+\mathbf{c}_1 \mathbf{c}_2=\mathbf{0}\)
The correct option among the following is

1 (A) is true, (R) is true and (R) is the correct explanation for (A).
2 (A) is true, (R) is true but (R) is not the correct explanation for (A).
3 (A) is true but (R) is false.
4 (A) is false but (R) is true.
TS EAMCET-11.09.2020
Three Dimensional Geometry

121180 If \(\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-7}{2}\) lies in the plane \(a x+b y\) \(+z=7\), then \(a+b=\)

1 -2
2 3
3 5
4 7
TS EAMCET-11.09.2020
For More Updates join with Us
Three Dimensional Geometry

121176 The angle between a line with direction ratios \(2,2,1\) and the line joining the points \((3,1,4)\) and \((7,2,12\) )

1 \(\cos ^{-1}\left(\frac{2}{3}\right)\)
2 \(\cos ^{-1}\left(\frac{3}{4}\right)\)
3 \(\tan ^{-1}\left(\frac{-2}{3}\right)\)
4 \(\cos ^{-1}\left(\frac{1}{3}\right)\)
AP EAMCET-21.04.2019
Three Dimensional Geometry

121177 The angle between the lines whose direction cosines satisfy the equations \(l+\mathbf{m}+\mathbf{n}=\mathbf{0}\) and \(l^2\) \(+\mathbf{m}^2-\mathbf{n}^2=\mathbf{0}\) is

1 \(\frac{\pi}{2}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{3}\)
AP EAMCET-05.10.2021
Three Dimensional Geometry

121178 Assertion (A) The direction ratios of line \(L_1\) are \(2,5,7\) and those of line \(L_2\) are \(\frac{4}{\sqrt{19}}, \frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}\). The lines \(\mathrm{L}_1, \mathrm{~L}_2\) are parallel.
Reason (R) The direction ratios of a line \(L_1\) are \(a_1, b_1, c_1\) and those of another line \(L_2\) are \(a_2, b_2\), \(c_2\). The lines \(L_1\) and \(L_2\) are parallel if \(a_1 a_2+b_1 b_2\) \(+\mathbf{c}_1 \mathbf{c}_2=\mathbf{0}\)
The correct option among the following is

1 (A) is true, (R) is true and (R) is the correct explanation for (A).
2 (A) is true, (R) is true but (R) is not the correct explanation for (A).
3 (A) is true but (R) is false.
4 (A) is false but (R) is true.
TS EAMCET-11.09.2020
Three Dimensional Geometry

121180 If \(\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-7}{2}\) lies in the plane \(a x+b y\) \(+z=7\), then \(a+b=\)

1 -2
2 3
3 5
4 7
TS EAMCET-11.09.2020