Find the point on the line  at a distance  from the point (1
    • Zigya Logo

    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

    Multiple Choice QuestionsShort Answer Type

    41. The equation of a line is fraction numerator 2 straight x minus 5 over denominator 4 end fraction space equals space fraction numerator straight y plus 4 over denominator 3 end fraction space equals fraction numerator 6 minus straight z over denominator 6 end fraction. Find the direction cosines of a line parallel to this line. 
    129 Views
    Answer

    Multiple Choice QuestionsLong Answer Type

    42. The cartesian equations of a line are 3 x + 1 = 6 y – 2 = 1 – z. Find the fixed point through which it passes, its direction ratios and also its vector equation.
    92 Views
    Answer

    Multiple Choice QuestionsShort Answer Type

    43. Find the equation of the line which passes through the point (3, 4, 5) and is parallel to the vector 2 straight i with hat on top plus 2 straight j with hat on top minus 3 straight k with hat on top.
    79 Views
    Answer
    44. Find the vector and Cartesian equations of the line through the point (5, 2, – 4) and which is parallel to the vector 3 straight i with overparenthesis on top space plus space 2 straight j with overparenthesis on top space minus space 8 space straight k with overparenthesis on top.
    74 Views
    Answer
    Advertisement
    45.

    Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector 3 straight i with overparenthesis on top space plus space 2 straight j with overparenthesis on top space minus space 2 straight k with overparenthesis on top.

    88 Views
    Answer
    46. Find equation of line, which is parallel to 2 straight i with hat on top plus straight j with hat on top minus straight k with hat on top and passes through (1, 2, 3).
    109 Views
    Answer
    47. Find the equation of a line, which is parallel to straight i with hat on top plus straight j with hat on top plus straight k with hat on top and passes through (2, 3, 1).
    96 Views
    Answer
    48. Find equation of a line, which is parallel to 2 straight i with hat on top space plus space straight j with hat on top space minus space 3 space straight k with hat on top and passes through (1, ,1, 1).
    97 Views
    Answer
    Advertisement

    Multiple Choice QuestionsLong Answer Type

    Advertisement
    Zigya App

    49. Find the point on the line fraction numerator straight x plus 2 over denominator 3 end fraction space equals space fraction numerator straight y plus 1 over denominator 2 end fraction space equals space fraction numerator straight z minus 3 over denominator 2 end fraction at a distance 3 square root of 2 from the point (1, 2, 3).

    Any point on the line  fraction numerator straight x plus 2 over denominator 3 end fraction space equals space fraction numerator straight y plus 1 over denominator 2 end fraction space equals space fraction numerator straight z minus 3 over denominator 2 end fraction space is space straight P left parenthesis 3 space straight r space minus space 2 comma space 2 straight r minus 1 comma space 2 straight r plus 3 right parenthesis.
    Distance of P from the point Q(1, 2, 3) is 3 square root of 2
    therefore                          PQ space equals space 3 square root of 2 space space space space space space space space space space space space space space space rightwards double arrow space space space PQ squared space equals space 18
    therefore              left parenthesis 3 straight r minus 2 minus 1 right parenthesis squared space plus space left parenthesis 2 straight r minus 1 minus 2 right parenthesis squared space space plus left parenthesis 2 straight r plus 3 minus 3 right parenthesis squared space equals space 18
    therefore space space space space left parenthesis 3 straight r minus 3 right parenthesis squared plus left parenthesis 2 straight r minus 3 right parenthesis squared plus left parenthesis 2 straight r right parenthesis squared space equals space 18 therefore space space space space 9 straight r squared minus 18 straight r plus 9 plus 4 straight r squared minus 12 straight r plus 9 plus 4 straight r squared space equals space 18 therefore space space space space 17 straight r squared minus 30 straight r space equals space 0 space space space or space space space straight r left parenthesis 17 straight r minus 30 right parenthesis space equals space 0 therefore space space space space space space space space space space space space space space space space space space space space space straight r space equals space 0 comma space space 30 over 17.
    when r = 0,  P is (-2, -1, 3)
    when straight r space equals space 30 over 7 comma space space space straight P space is space open parentheses 90 over 17 comma space minus 2 comma space 60 over 17 minus 1 comma space 60 over 17 plus 3 close parentheses space space space space straight i. straight e. space space space open parentheses 56 over 17 comma space 43 over 17 comma space 111 over 17 close parentheses
    therefore    required point is left parenthesis negative 2 comma space minus 1 comma space 3 right parenthesis space or space open parentheses 56 over 17 comma space 43 over 17 comma space 111 over 17 close parentheses.
    78 Views
  • Switch Icon Switch
    • Advertisement
    50. Find the vector and the Cartesian equations for the line through the points A (3, 4, –7) and B (5, 1, 6).
    77 Views
    Answer
    Advertisement
    Flag Popup Icon
    Flag it
    Submit
    Flag Popup Icon
    Switch to
    flexipad
    Share It Icon
    Share it
    Share It
    Share it