[" 1."x+2y=2],[quad 2x+3y=3]

Examine the consistency of the system of linear equtions in 1 to 6 x+2y=2 2x+3y=3

If A(x_1, y_1), B(x_2, y_2) and C(x_3, y_3) are vertices of an equilateral triangle whose each side is equal to 'a', then prove that, |[x_1, y_1, 2 ],[ x_2, y_2, 2],[ x_3, y_3, 2]|^2=3 a^4

if |[2a,x_1,y_1],[2b,x_2,y_2],[2c,x_3,y_3]|=(abc)/2!=0 then the area of the triangle whose vertices are (x_1/a,y_1/a),(x_2/b,y_2/b),(x_3/c,y_3/c) is (A) (1/4)abc (B) (1/8)abc (C) 1/4 (D) 1/8

A triangle has its three sides equal to a , b and c . If the coordinates of its vertices are A(x_1, y_1),B(x_2,y_2) \ a n d \ C(x_3,y_3), show that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=(a+b+c)(b+c-a)(c+a-b)(a+b-c)

A triangle has its three sides equal to a , b and c . If the coordinates of its vertices are A(x_1, y_1),B(x_2,y_2)a n dC(x_3,y_3), show that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=(a+b+c)(b+c-a)(c+a-b)(a+b-c)

The value of |[2x_1y_1, x_1y_2+x_2y_1, x_1y_3+x_3y_1], [x_1y_2+x_2y_1, 2x_2y_2, x_2y_3+x_3y_2], [x_1y_3+x_3y_1, x_2y_3+x_3y_2, 2x_3y_3]| is.

The value of |[2x_1y_1, x_1y_2+x_2y_1, x_1y_3+x_3y_1], [x_1y_2+x_2y_1, 2x_2y_2, x_2y_3+x_3y_2], [x_1y_3+x_3y_1, x_2y_3+x_3y_2, 2x_3y_3]| is.

Find the coordinates of the centroid of the triangle whose vertices are (x_1,y_1,z_1) , (x_2,y_2,z_2) and (x_3,y_3,z_3) .

Write the coordinate of the centroid of the triangle whose vertices are (x_1,y_1,z_1) , (x_2,y_2,z_2) and (x_3,y_3,z_3)

If the points (x_1, y_1),(x_2,y_2), and (x_3, y_3) are collinear show that (y_2-y_3)/(x_2x_3)+(y_3-y_1)/(x_3x_1)+(y_1-y_2)/(x_1x_2)=0