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Show that the lines (x-a+d)/(alpha-delt...

Show that the lines `(x-a+d)/(alpha-delta)=(y-a)/alpha=(z-a-d)/(alpha+delta)`and `(x-b+c)/(beta-gamma)=(y-b)/beta=(z-b-c)/(beta+gamma)`are coplanar.

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To show that the lines \[ \frac{x-a+d}{\alpha-\delta} = \frac{y-a}{\alpha} = \frac{z-a-d}{\alpha+\delta} \] and ...
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Knowledge Check

  • The lines (x-a+b)/(alpha-delta)=(y-a)/alpha=(z-a-d)/(alpha+delta), (x-b+c)/(beta-gamma)=(y-b)/beta=(z-a-d)/(beta+gamma) are coplanar, and the equation to the plane in which they lie is

    A
    `x+y+z=0`
    B
    `x-y+z=0`
    C
    `x-2y+z=0`
    D
    `x+y+z=0`

  • The lines (x-a+d)/(a-delta)=(y-a)/alpha=(z-a-d)/(a+delta) and (x-b+c)/beta-r=y-b/beta=z-b-c/beta+r are coplanar and then equation to the plane in which they lie is

    A
    x+y+z=0
    B
    x-y+z=0
    C
    x-2y+z=0
    D
    x+y-2z=0

  • The lines (x-a+d)/(a-delta)=(y-a)/alpha=(z-a-d)/(a+delta) and (x-b+c)/beta-r=y-b/beta=z-b-c/beta+r are coplanar and then equation to the plane in which they lie is

    A
    x+y+z=0
    B
    x-y+z=0
    C
    x-2y+z=0
    D
    x+y-2z=0
    • NCERT-THREE DIMENSIONAL GEOMETRY-SOLVED EXAMPLES
    1. Show that the lines (x-a+d)/(alpha-delta)=(y-a)/alpha=(z-a-d)/(alpha+...

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    2. Find the distance between the point P(6, 5, 9)and the plane determine...

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    3. Find the angle between the line (x+1)/2=y/3=(z-3)/6and the plane 10 ...

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    4. Find the equation of the plane that contains the point (1, 1, 2)and ...

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    5. A line makes angles alpha,beta,gamma and delta with the diagonals of...

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    6. Find the coordinates of the point where the line through the points A...

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    7. Find the vector equation for the line passing through the points (1, 0...

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    8. Find the vector and the Cartesian equations of the line through the p...

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    9. Show that the points A (2, 3, 4), B (1, 2, 3)and C (3, 8, 11)are co...

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    10. Find the direction cosines of x, y and z-axis.

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    11. Find the direction cosines of the line passing through the two points...

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    12. If a line has direction ratios 2,1,2.determine its direction cosines.

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    13. If a line makes angle 90^@, 60^@and 30^@with the positive direction ...

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    14. Find the angle between the pair of lines given by vecr=3 hat i+2 ha...

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    15. The Cartesian equation of a line is (x+3)/2=(y-5)/4=(z+6)/2. Find th...

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    16. Show that the lines (x+3)/(-3)=(y-1)/1=(z-5)/5and (x+1)/(-1)=(y-2)/2=(...

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    17. Find the vector equation of the plane passing through the intersectio...

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    18. Find the angle between the two planes 3x - 6y + 2z = 7and 2x + 2y - 2...

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    19. Find the angle between the two planes 2x + y 2z = 5and 3x 6y 2z = ...

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    20. Find the distance of a point (2, 5, 3)from the plane vecr.(6 hat i-...

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