Important Questions of Three Dimensional Geometry Mathematics | Zigya

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41.

A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance

  • 2H/A-B

  • H/A+B

  • H/2(A+B)

  • H/2(A+B)

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42.

The plane x + 2y – z = 4 cuts the sphere x2 + y2 + z2 – x + z – 2 = 0 in a circle of radius

  • 3

  • 1

  • 2

  • 2

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43.

Let A (2, –3) and B(–2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line

  • 2x + 3y = 9

  • 2x – 3y = 7

  • 3x + 2y = 5

  • 3x + 2y = 5

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44.

A line makes the same angle θ, with each of the x and z-axis. If the angle β, which it makes with y-axis, is such that sin2β = 3sin2θ , then cos2θ equals 

  • 2/3

  • 1/5

  • 3/5

  • 3/5

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45.

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

  • 3/2

  • 5/2

  • 7/2

  • 7/2

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46.

A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the point of intersection are given by

  • (3a, 3a, 3a), (a, a, a)

  • (3a, 2a, 3a), (a, a, a)

  • (3a, 2a, 3a), (a, a, 2a)

  • (3a, 2a, 3a), (a, a, 2a)

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47.

If the straight lines x = 1 + s, y = –3 – λs, z = 1 + λs and x = t/ 2 , y = 1 + t, z = 2 – t with parameters s and t respectively, are co-planar then λ equals

  • –2

  • –1

  • -1/2

  • -1/2

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48.

The intersection of the spheres x2 +y2 +z2 + 7x -2y-z =13 and x2 +y2 +z2 -3x +3y +4z = 8 is the same as the intersection of one of the sphere and the plane

  • x-y-z =1

  • x-2y-z =1

  • x-y-2z=1

  • x-y-2z=1

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49.

If the straight line y = mx + c (m > 0) touches the parabola y2 = 8(x + 2), then the minimum value taken by c is

  • 12

  • 8

  • 4

  • 4

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50.

The equation of the plane which contains the line of intersection of the planes x + y + z – 6 = 0 and 2x + 3y + z + 5 = 0 and perpendicular to the xy plane is:

  • x – 2y + 11 = 0

  • x + 2y + 11 = 0

  • x + 2y – 11 = 0

  • x + 2y – 11 = 0

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