Find the angle between the following pair of lines: from Mathem
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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.
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    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
    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
    79 Views
    Answer
    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

    The equations of two lines are
                                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 space straight z space equals space 5 space space space and space space space straight x over 1 space equals space fraction numerator 1 minus straight y over denominator 3 end fraction space equals space fraction numerator straight z minus 5 over denominator 2 end fraction

    or                    fraction numerator straight x minus 5 over denominator negative 3 end fraction space equals space fraction numerator straight y plus 3 over denominator negative 2 end fraction space equals space fraction numerator straight z minus 5 over denominator 0 end fraction space space space and space space space straight x over 1 space equals space fraction numerator straight y minus 1 over denominator negative 3 end fraction space equals space fraction numerator straight z minus 5 over denominator 2 end fraction
    Direction ratios of two lines are –3, –2, 0 and 1, –3, 2.
    Let θ be angle between the lines
    therefore space space space space space cos space straight theta space equals space fraction numerator left parenthesis negative 3 right parenthesis thin space left parenthesis 1 right parenthesis space plus space left parenthesis negative 2 right parenthesis thin space left parenthesis negative 3 right parenthesis space plus space left parenthesis 0 right parenthesis thin space left parenthesis 2 right parenthesis over denominator square root of 9 plus 4 plus 0 end root space square root of 1 plus 9 plus 4 end root end fraction space equals space fraction numerator negative 3 plus 6 plus 0 over denominator square root of 13 space square root of 14 end fraction space therefore space space space space space space cos space straight theta space equals space fraction numerator 3 over denominator square root of 182 end fraction space space space space space space space space rightwards double arrow space space space space space straight theta space equals space cos to the power of negative 1 end exponent open parentheses fraction numerator 3 over denominator square root of 182 end fraction close parentheses
    77 Views
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    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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