Angle Between Two Lines
Co-Ordinate system

88402 The value of the angle between two straight lines \(y=(2-\sqrt{3}) x+5\) and \(y=(2+\sqrt{3}) x-7\) is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(45^{\circ}\)
4 \(90^{\circ}\)
Co-Ordinate system

88403 The distance between the lines \(3 x+4 y=9\) and \(6 x+8 y=15\) is

1 \(3 / 2\)
2 \(3 / 10\)
3 6
4 \(3 / 5\)
Co-Ordinate system

88404 What is one of the angles between the straight lines
\((\mathrm{x} \cos \alpha-\mathrm{y} \sin \alpha)^{2}=\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right) \sin ^{2} \alpha\) ?

1 \(\alpha\)
2 \(2 \alpha\)
3 \(4 \alpha\)
4 \(\alpha / 2\)
Co-Ordinate system

88405 The distance between the lines \(3 x+4 y=9\) and \(6 x+8 y=15\) is equal to........units

1 \(\frac{1}{10}\)
2 \(\frac{3}{10}\)
3 \(\frac{5}{10}\)
4 \(\frac{7}{10}\)
Co-Ordinate system

88406 A tetrahedron has vertices \(\mathbf{P}(1,2,1), Q(2,1,3)\), \(R(-1,1,2)\) and \(O(0,0,0)\). The angle between the faces OPQ and PQR is

1 \(\cos ^{-1}\left(\frac{7}{31}\right)\)
2 \(\cos ^{-1}\left(\frac{9}{35}\right)\)
3 \(\cos ^{-1}\left(\frac{19}{35}\right)\)
4 \(\cos ^{-1}\left(\frac{17}{31}\right)\)
Co-Ordinate system

88402 The value of the angle between two straight lines \(y=(2-\sqrt{3}) x+5\) and \(y=(2+\sqrt{3}) x-7\) is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(45^{\circ}\)
4 \(90^{\circ}\)
Co-Ordinate system

88403 The distance between the lines \(3 x+4 y=9\) and \(6 x+8 y=15\) is

1 \(3 / 2\)
2 \(3 / 10\)
3 6
4 \(3 / 5\)
Co-Ordinate system

88404 What is one of the angles between the straight lines
\((\mathrm{x} \cos \alpha-\mathrm{y} \sin \alpha)^{2}=\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right) \sin ^{2} \alpha\) ?

1 \(\alpha\)
2 \(2 \alpha\)
3 \(4 \alpha\)
4 \(\alpha / 2\)
Co-Ordinate system

88405 The distance between the lines \(3 x+4 y=9\) and \(6 x+8 y=15\) is equal to........units

1 \(\frac{1}{10}\)
2 \(\frac{3}{10}\)
3 \(\frac{5}{10}\)
4 \(\frac{7}{10}\)
Co-Ordinate system

88406 A tetrahedron has vertices \(\mathbf{P}(1,2,1), Q(2,1,3)\), \(R(-1,1,2)\) and \(O(0,0,0)\). The angle between the faces OPQ and PQR is

1 \(\cos ^{-1}\left(\frac{7}{31}\right)\)
2 \(\cos ^{-1}\left(\frac{9}{35}\right)\)
3 \(\cos ^{-1}\left(\frac{19}{35}\right)\)
4 \(\cos ^{-1}\left(\frac{17}{31}\right)\)
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Co-Ordinate system

88402 The value of the angle between two straight lines \(y=(2-\sqrt{3}) x+5\) and \(y=(2+\sqrt{3}) x-7\) is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(45^{\circ}\)
4 \(90^{\circ}\)
Co-Ordinate system

88403 The distance between the lines \(3 x+4 y=9\) and \(6 x+8 y=15\) is

1 \(3 / 2\)
2 \(3 / 10\)
3 6
4 \(3 / 5\)
Co-Ordinate system

88404 What is one of the angles between the straight lines
\((\mathrm{x} \cos \alpha-\mathrm{y} \sin \alpha)^{2}=\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right) \sin ^{2} \alpha\) ?

1 \(\alpha\)
2 \(2 \alpha\)
3 \(4 \alpha\)
4 \(\alpha / 2\)
Co-Ordinate system

88405 The distance between the lines \(3 x+4 y=9\) and \(6 x+8 y=15\) is equal to........units

1 \(\frac{1}{10}\)
2 \(\frac{3}{10}\)
3 \(\frac{5}{10}\)
4 \(\frac{7}{10}\)
Co-Ordinate system

88406 A tetrahedron has vertices \(\mathbf{P}(1,2,1), Q(2,1,3)\), \(R(-1,1,2)\) and \(O(0,0,0)\). The angle between the faces OPQ and PQR is

1 \(\cos ^{-1}\left(\frac{7}{31}\right)\)
2 \(\cos ^{-1}\left(\frac{9}{35}\right)\)
3 \(\cos ^{-1}\left(\frac{19}{35}\right)\)
4 \(\cos ^{-1}\left(\frac{17}{31}\right)\)
Co-Ordinate system

88402 The value of the angle between two straight lines \(y=(2-\sqrt{3}) x+5\) and \(y=(2+\sqrt{3}) x-7\) is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(45^{\circ}\)
4 \(90^{\circ}\)
Co-Ordinate system

88403 The distance between the lines \(3 x+4 y=9\) and \(6 x+8 y=15\) is

1 \(3 / 2\)
2 \(3 / 10\)
3 6
4 \(3 / 5\)
Co-Ordinate system

88404 What is one of the angles between the straight lines
\((\mathrm{x} \cos \alpha-\mathrm{y} \sin \alpha)^{2}=\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right) \sin ^{2} \alpha\) ?

1 \(\alpha\)
2 \(2 \alpha\)
3 \(4 \alpha\)
4 \(\alpha / 2\)
Co-Ordinate system

88405 The distance between the lines \(3 x+4 y=9\) and \(6 x+8 y=15\) is equal to........units

1 \(\frac{1}{10}\)
2 \(\frac{3}{10}\)
3 \(\frac{5}{10}\)
4 \(\frac{7}{10}\)
Co-Ordinate system

88406 A tetrahedron has vertices \(\mathbf{P}(1,2,1), Q(2,1,3)\), \(R(-1,1,2)\) and \(O(0,0,0)\). The angle between the faces OPQ and PQR is

1 \(\cos ^{-1}\left(\frac{7}{31}\right)\)
2 \(\cos ^{-1}\left(\frac{9}{35}\right)\)
3 \(\cos ^{-1}\left(\frac{19}{35}\right)\)
4 \(\cos ^{-1}\left(\frac{17}{31}\right)\)
Co-Ordinate system

88402 The value of the angle between two straight lines \(y=(2-\sqrt{3}) x+5\) and \(y=(2+\sqrt{3}) x-7\) is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(45^{\circ}\)
4 \(90^{\circ}\)
Co-Ordinate system

88403 The distance between the lines \(3 x+4 y=9\) and \(6 x+8 y=15\) is

1 \(3 / 2\)
2 \(3 / 10\)
3 6
4 \(3 / 5\)
Co-Ordinate system

88404 What is one of the angles between the straight lines
\((\mathrm{x} \cos \alpha-\mathrm{y} \sin \alpha)^{2}=\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right) \sin ^{2} \alpha\) ?

1 \(\alpha\)
2 \(2 \alpha\)
3 \(4 \alpha\)
4 \(\alpha / 2\)
Co-Ordinate system

88405 The distance between the lines \(3 x+4 y=9\) and \(6 x+8 y=15\) is equal to........units

1 \(\frac{1}{10}\)
2 \(\frac{3}{10}\)
3 \(\frac{5}{10}\)
4 \(\frac{7}{10}\)
Co-Ordinate system

88406 A tetrahedron has vertices \(\mathbf{P}(1,2,1), Q(2,1,3)\), \(R(-1,1,2)\) and \(O(0,0,0)\). The angle between the faces OPQ and PQR is

1 \(\cos ^{-1}\left(\frac{7}{31}\right)\)
2 \(\cos ^{-1}\left(\frac{9}{35}\right)\)
3 \(\cos ^{-1}\left(\frac{19}{35}\right)\)
4 \(\cos ^{-1}\left(\frac{17}{31}\right)\)