If the foot of the perpendicular from the origin to plane is `P(a ,b ,c)` , the equation of the plane is a. `x/a=y/b=z/c=3` b. `a x+b y+c z=3` c. `a x+b y+c z=a^(2)+b^2+c^2` d. `a x+b y+c z=a+b+c`

From the point P(a ,b ,c), let perpendicualars P La n dP M be drawn to Y O Za n dZ O X planes, respectively. Then the equation of the plane O L M is a. x/a+y/b+z/c=0 b. x/a+y/b-z/c=0 c. x/a-y/b-z/c=0 d. x/a-y/b+z/c=0

The x-y plane is rotated about its line of intersection with the y-z plane by 45^0 , then the equation of the new plane is/are a. z+x=0 b. z-y=0 c. x+y+z=0 d. z-x=0

If in A B C , the distances of the vertices from the orthocentre are x, y, and z, then prove that a/x+b/y+c/z=(a b c)/(x y z)

Find the equation of the plane containing the line (y)/(b)+(z)/(c)=1,x=0 , and parallel to the line (x)/(a)-(z)/(c)1,y=0 .

If the volume of tetrahedron A B C D is 1 cubic units, where A(0,1,2),B(-1,2,1)a n dC(1,2,1), then the locus of point D is a. x+y-z=3 b. y+z=6 c. y+z=0 d. y+z=-3

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a) 1 (b) 2 (c) 3 (d) 4

The equation of the plane which has the property that the point Q(5,4,5) is the reflection of point P(1,2,3) through that plane, is a x+b y+c z=d where a, b , c, d in N . Find the least value of (a+b+c+d) .

Find the condition on a, b and c so that the following system of linear equations has one parameter family of solutions: x + y + z = a, x + 2y + 3z = b, 3x + 5y + 7z = c.

Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c x+a z b z+c y c z-a x-b y|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

The minimum value of P=b c x+c a y+a b z , when x y z=a b c , is