Divide: `35 a^2+32 a-99\ b y\ 7a-9` `a x^2+(b+a c)x+b c\ b y\ x+c`

Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the equation |a x-b y-c b x-a y c x+a b x+a y-a x+b y-cc y+b c x+a c y+b-a x-b y+c|=0 represents a straight line.

Show that |a b c a+2x b+2y c+2z x y z|=0

Add the following: 7a b c ,\ -5a b c ,\ 9a b c ,\ -8a b c 2x^2y ,\ -4x^2y ,\ 6x^2y ,\ -5x^2y

L_1=(a-b)x+(b-c)y+(c-a)=0L_2=(b-c)x+(c-a)y+(a-b)=0L_3=(c-a)x+(a-b)y+(b-c)=0 KAMPLE 6 Show that the following lines are concurrent L1 = (a-b) x + (b-c)y + (c-a) = 0 12 = (b-c)x + (c-a) y + (a-b) = 0 L3 = (c-a)x + (a-b) y + (b-c) = 0. ,

Evaluate each of the following algebraic expressions for x=1,\ y=-1, z=2,\ a=-2,\ b=1,\ c=-2: (i) a x+b y+c z (ii) a x^2+b y^2-c z^2 (iii) a x y+b y z+c x y

If x+y+z=0 prove that |a x b y c z c y a z b x b z c x a y|=x y z|a b cc a bb c a|

If a, b, c > 0 and x, y, z E R, then the determinant (a +a*)2 (a -ax)2 1 (b + b-y)2 (b b-y)2 1 (c2 + c2)2 (c+c2)2 1 x12 al roots of = 0, is is dependent on a. a, b, c only c. a, b, c, x, y, z b. x, y, z only d. None of these (-9: Let x < 1? then value of x2 +2 2x +1 1

The determinant |y^2-x y x^2a b c a ' b ' c '| is equal to a. |b x+a y c x+b y b^(prime)x+a ' y c^(prime)x+b ' y| b. |a x+b y b x+c y a^(prime)x+b ' y b ' x+c ' y| c. |b x+c y a x+b y b^(prime)x+c ' y a^(prime)x+b ' y| d. |a x+b y b x+c y a^(prime)x+b ' y b^(prime)x+c ' y|