which of the following pairs of points have a distance  43 ?

which of the following pairs of points have a distance  43 ?

  1. A

    (2,3, 5) and (4,3,1)

  2. B

    (-3,7,2) and (2, 4, -1)

  3. C

    (-1, 3, -4) and (1, -3, 4)

  4. D

    (2, -1, 3) and (-2,1, 3)

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    Solution:

    (a) Let the given points are A(2,3,5) and B(4,3,1).

              x1=2,y1=3,z1=5 and     x2=4,y2=3,z2=1

          Required distance

          AB=x2x12+y2y12+z2z12  AB=(42)2+(33)2+(15)2=4+0+16=20=25

    (b) Let the given points are A(- 3,7,2) and B(2,4, -1).

            Here,

          x1=3,y1=7,z1=2x2=2,y2=4,z2=1

             Required distance

             AB=x2x12+y2y12+z2z12=[2(3)]2+(47)2+(12)2=(2+3)2+(47)2+(12)2=25+9+9=43

    (c)  Let the given ,points  (-1, 3, -4) and (1, -3, 4)

           x1=1,y1=3,z1=4x2=1,y2=3,z2=4

           Required distance,

           AB=(1+1)2+(33)2+(4+4)2=4+36+64=104=226

    (d) Let the given points are A(2, -1,3) and B(-2,1,3).

           x1=2,y1=1,z1=3x2=2,y2=1,z2=3

             Required distance,

            AB=(22)2+(1+1)2+(33)2=42+22+0=16+4=20=25

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