सारिक `|[0,b^(2)a,c^(2)a],[a^(2)b,0,c^(2)b],[a^(2)c,b^(2)c,0]|" `Find the value of

Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

If [(a-b,2a+c),(2a-b,3c+d)]=[(-1, 5),( 0, 13)] , find the value of bdot

If a+b+c=0 and a^2+b^2+c^2=16 , find the value of a b+b c+c a

If a,b,c and A,B,C in R-{0} such that aA+bB+cD+ sqrt((a^(2)+b^(2)+c^(2))(A^(2)+B^(2)+C^(2)))=0 , then value of (aB)/(bA) +(bC)/(cB) + (cA)/(aC) is

Let a, b and c be such that a + b + c= 0 and P=a^(2)/(2a^(2)+ bc) + b^(2)/(2b^(2) + ca) + c^(2)/(2c^(2) + ab) is defined. What is the value of P.

If a^2+b^2+c^2=16 and a b+b c+c a=10 , find the value of a+b+c

If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ,b ,c in R) and are all different and nonzero), then prove that a+b+c=0.

If a^(2) + b^(2) + c^(3) + ab + bc + ca le 0 for all, a, b, c in R , then the value of the determinant |((a + b +2)^(2),a^(2) + b^(2),1),(1,(b +c + 2)^(2),b^(2) + c^(2)),(c^(2) + a^(2),1,(c +a +2)^(2))| , is equal to

If the quadrilateral formed by the lines a x+b y+c=0,a^(prime)x+b^(prime)y+c=0,a x+b y+c^(prime)=0,a^(prime)x+b^(prime)y+c^(prime)=0 has perpendicular diagonals, then b^2+c^2=b^('2)+c^('2) c^2+a^2=c^('2)+a^('2) a^2+b^2=a^('2)+b^('2) (d) none of these

If |(a-b-c, 2a, 2a),(2b, b-a-c, 2b),(2c, 2c, c-a-b)|=(a+b+c)(x+a+b+c)^2 then the value of x is equal to (A) -2(a+b+c) (B) a+b+c (C) -(a+b+c) (D) 2(a+b+c)