Find the angle between the pair of lines with direction ratios 2

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Advertisement

Three Dimensional Geometry

Long Answer Type

61. Find the vector equation of a line passing through a point with position vector

2 straight i with hat on top space minus space straight j with hat on top space plus space straight k with hat on top

and parallel to the line joining the points with position vectors

negative straight i with hat on top space plus space 4 space straight j with hat on top space plus space straight k with hat on top

and

straight i with hat on top space plus space 2 space straight j with hat on top space plus space 2 space straight k with hat on top

. Also, find the cartesian equivalent of this equations.

79 Views

Short Answer Type

62. The cartesian equations of a line are 6 x – 2 = – 3 y + 1 = 2 z = 2. Find the direction ratios of the line and write down the vector equation of the line through (2, – 1, –1) which is parallel to the given line.

90 Views

63. The points A (4, 5, 10), B (2, 3, 4) and C (1, 2, – 1) are three vertices of a parallelogram ABCD. Find vector and cartesian equations for the sides AB and BC and find the coordinates of D.

397 Views

Long Answer Type

64. A line passes through the point with position vector

2 space straight i with hat on top space minus space straight j with hat on top space plus space 4 space straight k with hat on top

and is in direction

straight i with hat on top space plus space straight j with hat on top space minus space 2 space straight k with hat on top.

Find equations for the line in vector and in cartesian form .

77 Views

Advertisement

65. Find the vector equation of a line passing through a point with position vector

straight i with hat on top space minus space 2 space straight j with hat on top space minus space 3 space straight k with hat on top

and parallel to the line joining the points with position vectors

straight i with hat on top space minus space straight j with hat on top space plus space 4 space straight k with hat on top

and

2 space straight i with hat on top space plus space straight j with hat on top space plus space space 2 space straight k with hat on top.

Also, find the cartesian equivalent of this equation.

80 Views

Short Answer Type

66. Find the angle between pair of lines:

straight r with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space 2 space straight j with hat on top space minus space 4 space straight k with hat on top space plus space straight lambda space left parenthesis straight i with hat on top space plus space 2 space straight j with hat on top space plus space 2 space straight k with hat on top right parenthesis

and

straight r with rightwards arrow on top space equals space 5 space straight i with hat on top space minus space 2 space straight k with hat on top space plus space straight mu space left parenthesis 3 space straight i with hat on top space plus space 2 space straight j with hat on top space plus space 6 space straight k with hat on top right parenthesis

75 Views

67. Find the angle between the pair of lines:

straight r with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space 5 space straight j with hat on top space plus space straight k with hat on top space plus space straight lambda space left parenthesis 3 space straight i with hat on top space plus space 2 space straight j with hat on top space plus space 6 space straight k with hat on top right parenthesis

and

straight r with rightwards arrow on top space equals space 7 space straight i with hat on top space minus space 6 space straight k with hat on top space plus space straight mu space left parenthesis straight i with hat on top space plus space 2 space straight j with hat on top space plus space 2 space straight k with hat on top right parenthesis

73 Views

68. Find the angle between the pair of lines:

straight r with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space straight j with hat on top space minus space 2 space straight k with hat on top space plus space straight lambda space left parenthesis straight i with hat on top space minus space straight j with hat on top space minus space 2 space straight k with hat on top right parenthesis

and

straight r with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space straight j with hat on top space minus space 5 space straight k with hat on top space plus space straight mu space left parenthesis 3 space straight i with hat on top space minus space 5 space straight j with hat on top space minus space 4 space straight k with hat on top right parenthesis

87 Views

Advertisement

Advertisement

69. Find the angle between the pair of lines with direction ratios 2, 2, 1 and 4, 1, 8.

The direction ratios of the two lines are 2, 2, 1 and 4, 1, 8.
Let θ be the angle between the two lines

therefore space space space space space space space cos space straight theta space equals space fraction numerator left parenthesis 2 right parenthesis thin space left parenthesis 4 right parenthesis space plus space left parenthesis 2 right parenthesis thin space left parenthesis 1 right parenthesis space plus space left parenthesis 1 right parenthesis thin space left parenthesis 8 right parenthesis over denominator square root of left parenthesis 2 right parenthesis squared plus left parenthesis 2 right parenthesis squared plus left parenthesis 1 right parenthesis end root space square root of left parenthesis 4 right parenthesis squared plus left parenthesis 1 right parenthesis squared plus left parenthesis 8 right parenthesis squared end root end fraction

open square brackets because space space cos space straight theta space equals space fraction numerator straight a subscript 1 straight a subscript 2 plus straight b subscript 1 straight b subscript 2 plus straight c subscript 1 straight c subscript 2 over denominator square root of straight a subscript 1 squared plus straight b subscript 1 squared plus straight c subscript 1 squared end root space space square root of straight a subscript 2 squared plus straight b subscript 2 squared plus straight c subscript 2 squared end root end fraction close square brackets

equals space fraction numerator 8 plus 2 plus 8 over denominator 3 cross times 9 end fraction space equals fraction numerator 18 over denominator 3 cross times 9 end fraction space equals 2 over 3

therefore

straight theta space equals space cos to the power of negative 1 end exponent space open parentheses 2 over 3 close parentheses

95 Views

Advertisement

70. Find the angle between the pair of lines with direction ratios 2, 6, 3 and 1, 2, 2.

98 Views

6
7
8

Advertisement