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Equation of any plane containing the lin...

Equation of any plane containing the line `(x-x_1)/(a)=(y-y_1)/(b)=(z-z_1)/(c)` is `A(x-x_1)+B(y-y_1)+C(z-z_1)=0` then pick correct alternatives

A

`(A)/(a)=(B)/(b)=(C)/(c)` is true for the line to be perpendicular to the plane.

B

`A(a+3)+B(b-1)+C(c-2)=0`

C

`2aA+3bB+4cC=0`

D

`Aa+Bb+Cc=0`

Text Solution

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The correct Answer is:
(a, d)
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The equation of the plane containing the line (x-x_(1))/(l)=(y-y_(1))/(m)=(z-z_(1))/(n) is a(x-x_(1))+b(y-y_(1))+c(z-z_(1))=0,backslash where (A) ax_(1)+by_(1)+cz_(1)=0(B)al+bm+cn=0(C)(a)/(l)=(b)/(m)=(c)/(n)(D)lx_(1)+my_(1)+nz_(1)=0

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Knowledge Check

  • The equation of the plane containing the line (x-x_1)/l=(y-y_1)/m=(z-z_1)/n is a(x-x_1)+b(y-y_1)+c(z-z_1)=0 where

    A
    `ax_1+by_1+cz_1=1`
    B
    `a/l=b/m=c/n`
    C
    `lx_1+my_1+nz_1=0`
    D
    al+bm+cn=0

  • The equation of the plane containing the lines (x-1)/2=(y+1)/-1=z/3 and x/2(y-2)/-1=(z+1)/3 is

    A
    `8x-y+5z-8=0`
    B
    `8x+y-5z-7=0`
    C
    `x-8y+3z+6=0`
    D
    `8x+y-5z+7=0`

  • The line (x-x_1)/(a_1)=(y-y_1)/(b_1)=(z-z_1)/(c_1) is parallel to the plane ax+by+cz+d=0 if

    A
    `(a_1)/(a)=(b_1)/(b)=(c_1)/( c)`
    B
    `aa_1+bb_1+cc_1=1`
    C
    `aa_1+bb_1+cc_1=0`
    D
    `a_1b_1c_1=a_2b_2c_2`

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