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the diagonals of the parallelogram forme...

the diagonals of the parallelogram formed by the the lines `a_1x+b_1y+c_1=0 ,a_1x+b_1y+c_1 '=0 , a_2x+b_2y+c_1=0 , a_2x+b_2y+c_1 '=0` will be right angles if:

Answer

Step by step text solution for the diagonals of the parallelogram formed by the the lines a_1x+b_1y+c_1=0 ,a_1x+b_1y+c_1 '=0 , a_2x+b_2y+c_1=0 , a_2x+b_2y+c_1 '=0 will be right angles if: by MATHS experts to help you in doubts & scoring excellent marks in Class 11 exams.

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Prove that the area of the parallelogram formed by the lines a_1x+b_1y+c_1=0,a_1x+b_1y+d_1=0,a_2x+b_2y+c_2=0, a_2x+b_2y+d_2=0, is |((d_1-c_1)(d_2-c_2))/(a_1b_2-a_2b_1)| sq. units.

Area of the parallelogram formed by the lines a_(1)x+b_(1)y+c_(1)=0,a_(1)x+b_(1)y+d_(1)=0 and a_(2)x+b_(2)y+c_(2)=0,a_(2)x+b_(2)y+d_(2)=0 is ([d_(1)-c_(1))(d_(2)-c_(2)))/([(a_(1)^(2)+b_(1)^(2))(a_(2)^(2)+b_(2)^(2))]^(1//2))

Knowledge Check

  • A : The area of the parallelogram formed by 4x-7y-13=0, 8x-y-39=0, 4x-7y+39=0, 8x-y+13=0 is 52. R : The area of the parallelogram formed by a_(1)x+b_(1)y+c_(1)=0, a_(1)x+b_(1)y+d_(1)=0, a_(2)x+b_(2)y+c_(2)=0, a_(2)x+b_(2)y+d_(2)=0 is |((c_(1)-d_(1))(c_(2)-d_(2)))/(a_(1)b_(2)-a_(2)b_(1))|

    A
    A, R are correct, R is correct explaination of A
    B
    A, R are correct, R is not correct explanation of A
    C
    A is true, R is false
    D
    A is false, R is true

  • a_1x+b_1y+c_1=0" and "a_2x+b_@y+c_2=0 are……..equations.

    A
    parallel
    B
    pair of linear
    C
    consistent
    D
    None

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    a_1x+b_1y+c_1=0 and a_2x+b_2y+c_2=0 has no solution if _________.

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