Find the value of p so that the lines from Mathematics Three Di
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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
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    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
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    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
     
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    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
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    Answer
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    Multiple Choice QuestionsLong Answer Type

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    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

    The equations of two lines are
                               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 fraction numerator straight z minus 3 over denominator 2 end fraction space space and space space fraction numerator 7 minus 7 straight x over denominator 3 space straight p end fraction space equals 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

    or                        fraction numerator straight x minus 1 over denominator negative 3 end fraction space equals space fraction numerator straight y minus 2 over denominator begin display style fraction numerator 2 straight p over denominator 7 end fraction end style end fraction space equals space fraction numerator straight z minus 3 over denominator 2 end fraction space space and space space fraction numerator straight x minus 1 over denominator negative begin display style fraction numerator 3 straight p over denominator 7 end fraction end style end fraction space equals space fraction numerator straight y minus 5 over denominator 1 end fraction space equals space fraction numerator straight z minus 6 over denominator negative 5 end fraction
    Direction ratios of two lines are
    negative 3 comma space space fraction numerator 2 straight p over denominator 7 end fraction comma space 2 space space and space minus fraction numerator 3 straight p over denominator 7 end fraction comma space 1 comma space minus 5
    ∵   lines are at right angle
    therefore         open parentheses negative 3 close parentheses space open parentheses negative fraction numerator 3 space straight p over denominator 7 end fraction close parentheses space plus space open parentheses fraction numerator 2 space straight p over denominator 7 end fraction close parentheses space left parenthesis 1 right parenthesis space plus space left parenthesis 2 right parenthesis thin space left parenthesis negative 5 right parenthesis space equals space 0

    therefore space space space space fraction numerator 9 space straight p over denominator 7 end fraction space plus space fraction numerator 2 space straight p over denominator 7 end fraction minus 10 space equals space 0 space space space space space space space space space rightwards double arrow space space space space fraction numerator 11 space straight p over denominator 7 end fraction space equals space 10 therefore space space space space space space space space space straight p space equals space 70 over 11
    80 Views
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    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. 
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    Answer
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