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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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Prove that the straight lines x/alpha=y/beta=z/gamma,x/l=y/m=z/n and x/(a alpha)=y/(b beta)=z/(c gamma) will be co planar if l/alpha(b-c)+m/beta(c-a)+n/gamma(a-b)=0

If |((beta+gamma-alpha -delta)^4 , (beta+gamma-alpha-delta)^2,1),((gamma+alpha-beta-delta)^4, (gamma+alpha-beta-delta)^2,1),((alpha+beta-gamma-delta)^4, (alpha + beta-gamma-delta)^2,1)|=-k(alpha -beta)(alpha -gamma)(alpha-delta)(beta-gamma)(beta-delta)(gamma-delta) , then the value of (k)^(1//2) is ____

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

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