AS triasngle is so placed thast the middle points of its sides re on tehaxes. If ,b,c be the length of its sides, show that the equation to its plane is `x/x_1+y/y_1+z/z_1. where 8x_1^2=b^2+c^2-a^2,8y_1^2=c^2+a^2-b^2 nd 8z_1^2=a^2+b^2-c^2`.

In a triangle /_\ XYZ, let a,b, c be the lengths o the sides opposite to the angle X,Y and Z respectively. If 1+cos2X-2cos2Y=2sinXsinY, then positive value (s) of a/b is (are

Solve the following system of equations by using determinants: x+y+z=1 , a x+b y+c z=k , a^2x+b^2y+c^2z=k^2

Solve the following system of equations by using determinants: x+y+z=1 , a x+b y+c z=k , a^2x+b^2y+c^2z=k^2 .

The vertex of a parabola is the point (a , b) and the latus rectum is of length l . If the axis of the parabola is parallel to the y-axis and the parabola is concave upward, then its equation is a. (x+a)^2=1/2(2y-2b) b. (x-a)^2=1/2(2y-2b) c. (x+a)^2=1/4(2y-2b) d. (x-a)^2=1/8(2y-2b)

findthe equationof the plane passing through the point (alpha, beta, gamma) and perpendicular to the planes a_1x+b_1y+c_1z+d_1=0 and a_2x+b_2y+c_2z+d_2=0

A variable plane passes through a fixed point(3,2,1) and meets and axes at A,B,C respectively. A plane is drawn parallel to plane through a second plane is drawn parallel to plane through A,B,C . Then the locus of the point of intersection of these three planes, is : (a) 1/x+1/y+1/z =11/6 (b) x/3+y/2+z/1=1 (c) 3/x+2/y+1/z=1 (d) xy+z=6

Show that the plane a x+b y+c z+d=0 divides the line joining the points (x_1, y_1, z_1)a n d(x_2, y_2, z_2) in the ratio (a x_1+b y_1+c z_1+d)/(a x_2+b y_2+c z_2+d) .

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 , ba n dc . 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)

Statement 1:If the point (2a-5,a^2) is on the same side of the line x+y-3=0 as that of the origin, then a in (2,4) Statement 2: The points (x_1, y_1)a n d(x_2, y_2) lie on the same or opposite sides of the line a x+b y+c=0, as a x_1+b y_1+c and a x_2+b y_2+c have the same or opposite signs.