Important Questions of Three Dimensional Geometry Mathematics | Zigya

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101.

If the planes r . 2i^ - λj^ + 3k^ = 0 and r . λi^ + 5j^ - k^ = 5  are perpendicular to each other, then the value of λ2 + λ is

  • 0

  • 2

  • 1

  • 3


102.

The cartesian form of the plane r = s - 2ti^ + 3 - tj^ + 2s + tk^ is

  • 2x - 5y -  z - 15 = 0

  • 2x - 5y +  z - 15 = 0

  • 2x - 5y -  z + 15 = 0

  • 2x + 5y -  z + 15 = 0


103.

Let P(- 7, 1, - 5) be a point on a plane and let O be the origin. If OP is normal to the plane, then the equation of the plane is

  • 7x - y + 5z + 75 = 0

  • 7x + y - 5z + 73 = 0

  • 7x + y + 5z + 73 = 0

  • 7x - y - 5z + 75 = 0


104.

The shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x2 + y2 + z2 + 4x - 2y - 6z = 155 is

  • 26

  • 11413

  • 13

  • 39


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105.

The point in the xy-plane which is equidistant from the point (2, 0, 3), (0, 3, 2) and (0, 0, 1) is

  • (1, 2, 3)

  • (- 3, 2, 0)

  • (3, - 2, 0)

  • (3, 2, 0)


106.

The angle between the line 3x - 13 = y +3- 1 = 5 - 2z4 and the plane 3x - 3y - 6z = 10 is equal to

  • π6

  • π4

  • π3

  • π2


107.

The angle between the straight lines r =2 - 3ti^ + 1 + 2tj^ + 2 + 6tk^ and r =1 + 4si^ + 2 - sj^ + 8s - 1k^ is

  • cos-14134

  • cos-12134

  • cos-14363

  • cos-13463


108.

If Q is the image of the point P(2, 3, 4) under the reflection in the plane x - 2y + 5z = 6, then the equation of the line PQ is

  • x - 2- 1 = y - 32 = z - 45

  • x - 21 = y - 3- 2 = z - 45

  • x - 2- 1 = y - 3- 2 = z - 45

  • x - 21 = y - 32 = z - 45


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109.

The distance of the point of intersection of the line x - 23 = y + 14 = z - 212 and the plane x - y + z = 5 from the point (- 1, - 5, - 10)is

  • 13

  • 12

  • 11

  • 8


110.

If the direction cosines of a line are 1c, 1c, 1c, then

  • 0 < c < 1

  • c > 2

  • c = ± 2

  • c = ± 3


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