Important Questions of Three Dimensional Geometry Mathematics | Zigya

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

Advertisement
471.

The equation of the plane which is equidistant from the two parallel planes 2x - 2y + z + 3= 0 and 4x - 4y + 2z + 9 = 0 is

  • 8x - 8y + 4z + 15 = 0

  • 8x - 8y + 4z - 15 = 0

  • 8x - 8y + 4z + 3 = 0

  • 8x - 8y + 4z - 3 = 0


472.

The angle between the planes 3x + 4y + 5z = 3 and 4x - 3y + 5z = 9 is equal to

  • π2

  • π4

  • π6

  • π3


473.

The vector equation of the plane through the point (2, 1, - 1) and parallel to the plane r - (i + 3j - k) = 0 is

  • r . (i + 9j + 11k) = 6

  • r . (i - 9j + 11k) = 4

  • r . (i + 3j - k) = 6

  • r . (i + 3j - k) = 4


474.

If the foot of the perpendicular drawn from the point (5, 1, - 3) to a plane is (1, - 1, 3), then the equation of the plane is

  • 2x + y - 3z + 8 = 0

  • 2x + y + 3z + 8 = 0

  • 2x - y - 3z + 8 = 0

  • 2x - y + 3z + 8 = 0


Advertisement
475.

The equation of the plane through the line of intersection of the planes x - y + z + 3 = 0 and x + y + 22 + 1 = 0 and parallel to x-axis is

  • 2y - z = 2

  • 2y + z = 2

  • 4y + z = 4

  • y - 2z = 3


476.

If 3p + 2q = i + j + k and 3p - 2q = i - j - k, then the angle between p and q is

  • π6

  • π4

  • π3

  • π2

     


477.

The point of intersection of the straight line x - 22 = y - 1- 3 = z + 21 with the plane x + 3y - z + 1 = 0 is

  • (3, - 1, 1)

  • (- 5, 1, - 1)

  • (2, 0, 3)

  • (4, - 2, - 1)


478.

If the lines 2x - 12 = 3 - y1 = z - 13 and x + 32 = z + 1p = y + 25 are perpendicular to each other, then p is equal to

  • 1

  • - 1

  • 10

  • 75


Advertisement
479.

The point P(x, y, z) lies in the first octant and its distance from the origin is 12 units. If the position vector of P make 45° and 60° with the x-axis and y-axis respectively, then the coordinates of P are

  • 33, 6, 32

  • 43, 8, 42

  • 62, 6, 6

  • 6, 6, 62


480.

The distance between the planes r . (i + 2j - 2k) + 5 = 0 and r . (2i + 4j - 4k) - 16 = 0 is

  • 3

  • 113

  • 13

  • 133


Advertisement