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Given the equation of the line 3x-y+z+1=...

Given the equation of the line `3x-y+z+1=0 and 5x-y+3z=0`. Then,which of the following is correct?

A

Symmetrical form of the equation of line is `(x)/(2)=(y-(1)/(8))/(-1)=(z+(5)/(8))/(1)`.

B

Symmetrical form of the equation of line is `(x+(1)/(8))/(1)=(y-(5)/(8))/(-1)=(z)/(-2)`

C

Equation of the through `(2, 1, 4)` and perpencular to the given lines is `2x-y+z-7=0`.

D

Equation of the plane through `(2, 1, 4)` and perpendicular to the given lines is `x+y-2z+5=0`.

Text Solution

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The correct Answer is:
(b, d)
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Find the equation of the plane which contains the line of intersection of the planes x+2y+3z-4=0 and 2x+y-z+5=0 and which is perpendicular to the plane 5x+3y-6z+8=0

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Knowledge Check

  • The symmetric equation of lines 3x+2z-5=0 and x+y-2z-3=0 is

    A
    `(x-1)/(5)=(y-4)/(7)=(z-0)/(1)`
    B
    `(x+1)/(5)=(y+4)/(7)=(z-0)/(1)`
    C
    `(x+1)/(-5)=(y+4)/(7)=(z-0)/(1)`
    D
    `(x-1)/(-5)=(y-4)/(7)=(z-0)/(1)`

  • The symmetric equation of lines 3x+2y+z-5=0 and x+y-2z-3=0 is

    A
    `(x-1)/5=(y-4)/7=(z-0)/1`
    B
    `(x+1)/5=(y+4)/7=(z-0)/1`
    C
    `(x+1)/-5=(y-4)/7=(z-0)/1`
    D
    `(x-1)/-5=(y-4)/7=(z-0)/1`

  • If x ^(3) + y ^(2) + z ^(3) = 3xyz and x + y + z ne 0 then which of the following is correct ?

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

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