Important Questions of Three Dimensional Geometry Mathematics | Zigya

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201.

The number of solutions of the equation tan(x) + sec(x) = 2cos(x) and cos(x)  0 lying in the interval (0, π) is :

  • 2

  • 1

  • 0

  • 3


202.

The angle between a and b is 5π6 and the projection of a in the direction of b is - 63, then a is equal to :

  • 6

  • 32

  • 12

  • 4


203.

A unit vector in the plane of i^ + 2j^ + k^ and i^ + j^ + 2k^ and perpendicular yo 2i^ + j^ + k^ is :

  • j^ - k^

  • i^ + j^2

  • j^ + k^2

  • j^ - k^2


204.

The equation of the plane through the point (2, - 1, - 3) and parallel to the lines x - 13 = y + 22 = z- 4 and x2 = y - 1- 3 = z - 22 is :

  • 8x + 14y + 13z + 37 = 0

  • 8x - 14y + 13z + 37 = 0

  • 8x + 14y - 13z + 37 = 0

  • 8x + 14y + 13z - 37 = 0


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205.

If for a plane, the intercepts on the co-ordinate axes are 8, 4, 4, then the length of the perpendicular from the origin on to the plane is :

  • 83

  • 38

  • 3

  • 43


206.

If a plane meets the co-ordinate axes at A, B and C such that the centroid of the triangle is (1, 2, 4), then the equation of the plane is:

  • x + 2y + 4z = 12

  • 4x + 2y + z = 12

  • x + 2y + 4z = 3

  • 4x + 2y + z = 3


207.

The position vector of the point where the line r = i^ + j^ - k^ + ti^ + j^ - k^ meets the plane r . i^ + j^ - k^ = 5 is :

  • 5i^ + j^ - k^

  • 5i^ + 3j^ - 3k^

  • 2i^ + j^ + 2k^

  • 5i^ + j^ + k^


208.

If the distance of the point (1, 1, 1) from the origin is half its distance from the plane x + y + z+ k = 0, then k is equal to :

  • ± 3

  • ± 6

  • - 3, 9

  • 3, - 9


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209.

The angle between the line x - 32 = y - 11 = x + 4- 2 and the plane, x + y + z + 5 = 0 is :

  • sin-123

  • sin-113

  • π4

  • sin-1133


210.

The point of intersection of the line r = 7i^ + 10j^ + 13k^ + s2i^ + 3j^ + 4k^ and r = 3i^ + 5j^ + 7k^ + si^ + 2j^ + 3k^ is :

  • i^ + j^ - k^

  • 2i^ - j^ + 4k^

  • i^ - j^ + k^

  • i^ + j^ + k^


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