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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.

A

0

B

1

C

`sqrt(a^(2)+c^(2))`

D

`sqrt(d^(2)+f^(2))`

Text Solution

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The correct Answer is:
A
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Show that the lines (x-a+d)/(alpha-delta)=(y-a)/(alpha)=(z-a-d)/(alpha+delta)(x-b+c)/(beta-gamma)=(y-b)/(beta)=(z-b-c)/(beta+gamma) are coplanar.

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

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

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    `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

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    x+y+z=0
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  • 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

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