Find the angle between pair of lines:                 
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    Three Dimensional Geometry

    Multiple Choice QuestionsShort Answer Type

    71. Find the angle between the lines whose direction ratios are a, b, c and b – c, c – a, a – b.
    74 Views
    Answer
    72. Find the angle between each of the following pairs of lines:
    fraction numerator straight x minus 2 over denominator 3 end fraction space equals space fraction numerator straight y plus 1 over denominator negative 2 end fraction comma space space straight z space equals space 2 comma space space space fraction numerator straight x minus 1 over denominator 1 end fraction space equals space fraction numerator 2 straight y plus 3 over denominator 3 end fraction space equals space fraction numerator straight z plus 5 over denominator 2 end fraction
    84 Views
    Answer
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    73. Find the angle between pair of lines:
                       fraction numerator straight x plus 3 over denominator 3 end fraction space equals space fraction numerator straight y minus 1 over denominator 5 end fraction space equals space fraction numerator straight z plus 3 over denominator 4 end fraction

    and          fraction numerator straight x plus 1 over denominator 1 end fraction space equals space fraction numerator straight y minus 4 over denominator 1 end fraction space equals space fraction numerator straight z minus 5 over denominator 2 end fraction

    The equation of lines are
                                    fraction numerator straight x plus 3 over denominator 3 end fraction space equals space fraction numerator straight y minus 1 over denominator 5 end fraction space equals space fraction numerator straight z plus 3 over denominator 4 end fraction

    and                         fraction numerator straight x plus 1 over denominator 1 end fraction space equals space fraction numerator straight y minus 4 over denominator 1 end fraction space equals space fraction numerator straight z minus 5 over denominator 2 end fraction
    Direction-ratios of the two lines are 3, 5, 4 and 1,1, 2.
    Let θ be the angle between the lines.
    therefore space space space cos space straight theta space equals space fraction numerator left parenthesis 3 right parenthesis left parenthesis 1 right parenthesis space plus space left parenthesis 5 right parenthesis left parenthesis 1 right parenthesis space plus space left parenthesis 4 right parenthesis left parenthesis 2 right parenthesis over denominator square root of left parenthesis 3 right parenthesis squared plus left parenthesis 5 right parenthesis squared plus left parenthesis 4 right parenthesis squared end root space square root of left parenthesis 1 right parenthesis squared plus left parenthesis 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root end fraction space space space space space space space space space space space space space space space space space equals space fraction numerator 3 plus 5 plus 8 over denominator square root of 50 square root of 6 end fraction space equals space fraction numerator 16 over denominator 5 square root of 2 space square root of 6 end fraction space equals space fraction numerator 16 over denominator 5 square root of 2. space square root of 2 space square root of 3 end fraction space equals space fraction numerator 8 over denominator 5 square root of 3 end fraction space equals space fraction numerator 8 square root of 3 over denominator 15 end fraction therefore space space space space straight theta space equals space cos space to the power of negative 1 end exponent space open parentheses fraction numerator 8 square root of 3 over denominator 15 end fraction close parentheses
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    74. Find the angle between the following pair of lines:
    fraction numerator straight x minus 2 over denominator 2 end fraction space equals space fraction numerator straight y minus 1 over denominator 5 end fraction space equals fraction numerator straight z plus 3 over denominator negative 3 end fraction space space and space space fraction numerator straight x plus 1 over denominator negative 1 end fraction space equals space fraction numerator straight y minus 4 over denominator 8 end fraction space equals space fraction numerator straight z minus 5 over denominator 4 end fraction
    95 Views
    Answer
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    75. Find the angle between the following pair of lines:
    fraction numerator 5 minus straight x over denominator 3 end fraction space equals space fraction numerator straight y plus 3 over denominator negative 2 end fraction comma space space straight z space equals space 5 space space space and space space straight x over 1 space equals space fraction numerator 1 minus straight y over denominator 3 end fraction space equals fraction numerator straight z minus 5 over denominator 2 end fraction
    77 Views
    Answer
    76. Find the angle between the following pair of lines:
     straight x over 2 space equals space straight y over 2 space equals space straight z over 1 space space and space space fraction numerator straight x minus 5 over denominator 4 end fraction space equals space fraction numerator straight y minus 2 over denominator 1 end fraction space equals space fraction numerator straight z minus 3 over denominator 8 end fraction
    87 Views
    Answer
    77. Find the angle between the following pair of lines:
    fraction numerator straight x minus 5 over denominator 1 end fraction equals space fraction numerator 2 straight y plus 6 over denominator negative 2 end fraction space equals space fraction numerator straight z minus 3 over denominator 1 end fraction space space and space fraction numerator straight x minus 2 over denominator 3 end fraction space equals space fraction numerator straight y plus 1 over denominator 4 end fraction space equals space fraction numerator straight z minus 6 over denominator 5 end fraction
     
    84 Views
    Answer
    78. Find the angle between the lines
    straight x over 1 space equals fraction numerator negative straight y over denominator 0 end fraction space equals space fraction numerator straight z over denominator negative 1 end fraction space space and space space straight x over 3 space equals space straight y over 4 space equals straight z over 5
    81 Views
    Answer
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    Multiple Choice QuestionsLong Answer Type

    79. Find the value of p so that the lines
    fraction numerator 1 minus straight x over denominator 3 end fraction space equals space fraction numerator 7 straight y minus 14 over denominator 2 space straight p end fraction space equals space fraction numerator straight z minus 3 over denominator 2 end fraction space space and space space fraction numerator 7 minus 7 straight z over denominator 3 space straight p end fraction space equals space fraction numerator straight y minus 5 over denominator 1 end fraction space equals space fraction numerator 6 minus straight z over denominator 5 end fraction
    80 Views
    Answer

    Multiple Choice QuestionsShort Answer Type

    80. Show that the lines
    fraction numerator straight x minus 5 over denominator 7 end fraction space equals space fraction numerator straight y plus 2 over denominator negative 5 end fraction space equals straight z over 1 space and space straight x over 1 space equals space straight y over 2 space equals space straight z over 3 are prependicular to each other. 
    85 Views
    Answer
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