If the plane 2ax − 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres
x2 + y2 + z2 + 6x − 8y − 2z = 13 and x2 + y2 + z2 − 10x + 4y − 2z = 8, then a equals
-1
1
-2
-2
C.
-2
Plane 2ax – 3ay + 4az + 6 = 0 passes through the mid point of the centre of spheres x2 + y2 + z2 + 6x – 8y – 2z = 13 and x2 + y2 + z2 – 10x + 4y – 2z = 8 respectively centre of spheres are (-3, 4, 1) & (5, - 2, 1) Mid point of centre is (1, 1, 1) Satisfying this in the equation of plane,
we get 2a – 3a + 4a + 6 = 0
⇒ a = -2.
If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is
(-1, 7/3)
(-1/3, 7/3)
(1, 7/3)
(1, 7/3)
Let a, b and c be distinct non-negative numbers. If the vectors
the Geometric Mean of a and b
the Arithmetic Mean of a and b
equal to zero
equal to zero
If are non -coplanar vector λ is a real number then
exactly one value of λ
no value of λ
exactly three values of λ
exactly three values of λ
Three houses are available in a locality. Three persons apply for the houses. Each applies to one house without consulting others. The probability that all the three apply for the same house is
2/9
1/9
8/9
8/9