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Three Dimension...

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  • Question 1
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    Direction cosines of a line are

  • Question 2
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    Shortest distance between two skew lines is

  • Question 3
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    Find the shortest distance between the lines  

  • Question 4
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    The angle  θbetween the planes A1 x + B1 y + C1 z + D1 = 0 and A2 x + B2 y + C2 z + D2 = 0 is given by

  • Question 5
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    Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x –y + z = 0.

  • Question 6
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    If l, m, n are the direction cosines of a line, then

  • Question 7
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    Shortest distance between  

  • Question 8
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    Find the shortest distance between the lines :   

  • Question 9
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    The distance of a point whose position vector is    from the plane

  • Question 10
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    Find the angle between the planes whose vector equations are

  • Question 11
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    is a vector joining two points P(x1 , y1 , z1 ) and Q(x2 , y2 , z2 ). If  Direction cosines of  are

  • Question 12
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    Shortest distance between the lines  

  • Question 13
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    Find the shortest distance between the lines    and  

  • Question 14
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    The distance d from a point P(x1 , y1 , z1 ) to the plane Ax + By + Cz + D = 0 is

  • Question 15
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    Determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.7x + 5y + 6z + 30 = 0 and 3x –y –10z + 4 = 0

  • Question 16
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    If l, m and n are the direction cosines of a line, Direction ratios of the line are the numbers which are

  • Question 17
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    Distance between  

  • Question 18
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    Find the angle between the following pairs of lines:   and  

  • Question 19
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    Determine the direction cosines of the normal to the plane and the distance from the origin. Plane z = 2

  • Question 20
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    In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z –2 = 0 and x –2y + 5 = 0

  • Question 21
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    If l, m, n are the direction cosines and a, b, c are the direction ratios of a line then

  • Question 22
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    If a line makes angles  90∘ , 135∘ , 45∘ with the x, y and z –axes respectively, find its direction cosines.

  • Question 23
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    In the vector form, equation of a plane which is at a distance d from the origin, and   is the unit vector normal to the plane through the origin is

  • Question 24
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    Determine the direction cosines of the normal to the plane and the distance from the origin. Plane x + y + z = 1

  • Question 25
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    In the following case, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. 2x –2y + 4z + 5 = 0 and 3x –3y + 6z –1 = 0

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