For `0 < varphigeqpi/2,ifx=sum_(n=0)^oocos^(2n)varphi,y=sum_(n=0)^oosin^(2n)varphi,t h e n` (a)`x y z=x z+y` (b) `x y z=x y+z` (c)`x y z=x+y+z` (d) `x y z=y z+x`

Find the area of the triangle vertices are (0, 0), (3, 0) and (0, 2)

The straight line a x+b y+c=0 , where a b c!=0, will pass through the first quadrant if (a) a c >0,b c >0 (b) ac >0 or b c 0 or a c >0 (d) a c<0 or b c<0

The position vectors of the four angular points of a tetrahedron OABC are (0, 0, 0); (0, 0,2) , (0, 4,0) and (6, 0, 0) respectively. A point P inside the tetrahedron is at the same distance r from the four plane faces of the tetrahedron. Find the value of r

Four distinct points (2k,3k),(1,0),(0,1)and(0,0) lie on a circle for

Plot the following ordered pairs on a graph sheet. What do you observe? (i) (1,0), (3,0), (-2,0), (-5,0), (0,0), (5,0), (-6,0) (ii) (0,1),(0,3),(0,-2),(0,-5),(0,0),(0,5),(0,-6)

The z-coordinate of a point equidistant from the points ( 0 , 0 ,0) , ( 2 , 0 , 0) , ( 0 , 4 , 0) and ( 0 , 0, 6) is _

Determine the coordinates of the point which is equiistant from the points ( 0 , 0 0) , ( a , 0 ,0) and ( 0 , b , 0) and ( 0 , 0 , c) .

Find the co-ordinate of the point which is equidistance from (alpha, 0, 0) , (0,beta,0) , (0,0,gamma) and (0,0,0).

Find the coordinates of the point which is equidistant from the points ( 0 , 0 ,0) , ( 6 , 0 ,0) , ( 0 , - 4 , 0) and ( 0 , 0 , -2) .

Find the equation of the sphere passing through (0,0,0),(1,0,0),(0,1,0) and (0,0,1)dot