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if the lines ax + by + c=0,bx+cy+a=0 and cx+ay+b=0 be concurrent then A.a^3+b^3+c^3-3abc=0 B. a^3+b^3+c^3-abc C.a^3+b^3+c^3+3abc. D.none of these Sir pls explain the answer in detail. Thanks and regards, Jai

if the lines ax + by + c=0,bx+cy+a=0 and cx+ay+b=0 be concurrent then
A.a^3+b^3+c^3-3abc=0 B. a^3+b^3+c^3-abc
C.a^3+b^3+c^3+3abc.    D.none of these
Sir pls explain the answer in detail. 
Thanks and regards,
Jai

Grade:12

5 Answers

siddharth gupta
28 Points
7 years ago
CONCURRENCY OF LINES IS DETERMINED BY USING the ZERO or NON-ZERO VALUE OF THE DETERMINANT
                                            a1      b1        c1
                                            a2      b2      c2
                                            a3      b3      c3 WHICH IS ZERO FOR CONCUREENT LINES.
WHICH IN THIS CASE IS :
                                            a        b        c
                                            b        c        a
                                            c        a        b
THIS IS A SPECIAL DETERMINANT WHOSE VALUE IS 3abc-a3-b3-c3 and in this case it’s value is 0(lines being concurrent ) therefore a3+b3+c3=3abc.
WITH REGARDS
SIDDHARTH GUPTA
siddharth gupta
28 Points
7 years ago
CONCURRENCY OF LINES IS DETERMINED BY USING the ZERO or NON-ZERO VALUE OF THE DETERMINANT
                                            a1      b1        c1
                                            a2      b2      c2
                                            a3      b3      c3 WHICH IS ZERO FOR CONCUREENT LINES.
WHICH IN THIS CASE IS :
                                            a        b        c
                                            b        c        a
                                            c        a        b
THIS IS A SPECIAL DETERMINANT WHOSE VALUE IS 3abc-a3-b3-c3 and in this case it’s value is 0(lines being concurrent ) therefore a3+b3+c3=3abc.
WITH REGARDS
SIDDHARTH GUPTA
siddharth gupta
28 Points
7 years ago
CONCURRENCY OF LINES IS DETERMINED BY USING the ZERO or NON-ZERO VALUE OF THE DETERMINANT
                                            a1      b1        c1
                                            a2      b2      c2
                                            a3      b3      c3 WHICH IS ZERO FOR CONCUREENT LINES.
WHICH IN THIS CASE IS :
                                            a        b        c
                                            b        c        a
                                            c        a        b
THIS IS A SPECIAL DETERMINANT WHOSE VALUE IS 3abc-a3-b3-c3 and in this case it’s value is 0(lines being concurrent ) therefore a3+b3+c3=3abc.
WITH REGARDS
SIDDHARTH GUPTA
siddharth gupta
28 Points
7 years ago
CONCURRENCY OF LINES IS DETERMINED BY USING the ZERO or NON-ZERO VALUE OF THE DETERMINANT
                                            a1      b1        c1
                                            a2      b2      c2
                                            a3      b3      c3 WHICH IS ZERO FOR CONCUREENT LINES.
WHICH IN THIS CASE IS :
                                            a        b        c
                                            b        c        a
                                            c        a        b
THIS IS A SPECIAL DETERMINANT WHOSE VALUE IS 3abc-a3-b3-c3 and in this case it’s value is 0(lines being concurrent ) therefore a3+b3+c3=3abc.
WITH REGARDS
SIDDHARTH GUPTA
siddharth gupta
28 Points
7 years ago
CONCURRENCY OF LINES IS DETERMINED BY USING the ZERO or NON-ZERO VALUE OF THE DETERMINANT
                                            a1      b1        c1
                                            a2      b2      c2
                                            a3      b3      c3 WHICH IS ZERO FOR CONCUREENT LINES.
WHICH IN THIS CASE IS :
                                            a        b        c
                                            b        c        a
                                            c        a        b
THIS IS A SPECIAL DETERMINANT WHOSE VALUE IS 3abc-a3-b3-c3 and in this case it’s value is 0(lines being concurrent ) therefore a3+b3+c3=3abc.
WITH REGARDS
SIDDHARTH GUPTA

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