Three Dimension...

Which of the following statements regarding the three pairs of lines is/are correct?

(i)
(ii)  and
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The equation xy = 0 in three dimensional space represents

If  and  are the roots of the quadratic equation ax² + bx + c = 0 and the plane  is passing through the line of intersection of the two planes  and , then the value of b is

If the plane 2ax - 3ay + 4az + 6 = 0 passes through the mid-point 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

The distance of the point ( x , y , z ) from the XY –plane is

Equation of the sphere which circumscribes the tetrahedron with vertices O (0, 0, 0), A (1, 0, 0), B (0, 1, 0), C (0, 0, 1) is

In three dimensional space, locus of the equation x²+z²=0 is

Directions: The following question has four choices, out of which ONE or MORE is/are correct.

If a³ + za² + ya + x = 0, b³ + zb² + yb + x = 0 and c³ + zc² + yc + x = 0, which of the following statements is/are wrong?

Directions: The following question has four choices, out of which ONLY ONE is correct.

An equilateral triangle ABC has each side of length `1` unit. Let M and N be two points respectively on the sides AB and AC such that  and  If  and  are orthogonals, the value of K is equal to

Directions: The following question has four choices, out of which ONE or MORE are correct.

Let PM be a perpendicular from the point P (1, 2, 3) to x-y plane. If OP makes an angle with the positive direction of z-axis and OM makes an angle with the positive direction of x-axis, where O is the origin (and are acute angles), then

The equation of sphere concentric with the sphere x² + y² + z² – 4x – 6y – 8z – 5 = 0 and which passes through origin is

If P (x, y, z) is a point on the line segment joining Q (2, 2, 4) and R (3, 5, 6) such that projections of on the axes are , respectively, then in what ratio does P divide ?

The equation of the sphere circumscribing the tetrahedron whose faces are x = 0, y = 0, z = 0 and  is

The graph of the equation x²+y²=0 in the three dimensional space is

Directions: The following question has four choices, out of which ONLY ONE is correct.

A force of  unit acts along the line . The moment of this force about the point (4, 1) along positive z - axis is

The distance of the point (1, 0, – 3) from the plane x – y – z = 9 measured parallel to the line  =  =  is

The radius of the circle in which the sphere x² + y² + z² + 2x - 2y - 4z - 19 = 0 is cut by the plane x + 2y + z + 7 = 0 is

Let AB be the straight line . From a point P (1, 2, 5), a straight line PQ is drawn parallel to the plane 3x + 4y + 5z = 0 to meet AB in Q. Then, the equation of PQ is

The angle between the lines x = 1 , y = 2 and y = - 1 , z = 0 is