Self Studies

Three Dimension...

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  • Question 1
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    Find the direction cosines of a line which makes equal angles with all three the coordinate axes.​

  • Question 2
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    Three planes, viz the XY Plane, XZ Plane and the YZ Plane divide the space into eight parts. Each part is called an OCTANT. What is the relation between these three planes ​

  • Question 3
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    The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:​

  • Question 4
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    If the direction cosines of a line from the positive X-axis and Y-axis areThe angle of the line through Z-axis is:​

  • Question 5
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    The direction cosines of the line equally inclined with the axes are:​

  • Question 6
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    The direction cosines of the line whose direction ratios are 6, –6, 3 are:

  • Question 7
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    Find the direction cosines of the x axis.​

  • Question 8
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    The direction cosines of the line joining the points (2, -1, 8) and (-4, -3, 5) are:

  • Question 9
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    What are direction numbers of a line.​

  • Question 10
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    What are direction ratios of a line.​

  • Question 11
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    Find the direction cosines of the side AB of the triangle whose vertices are A(3, 5, -4), B(-1, 1, 2) and C(-5, -5, -2)

  • Question 12
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    If l, m , n are the direction cosines of any line, then sum of the squares of the direction cosines of the line is always ​

  • Question 13
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    If a line has the direction ratios -4, 18, -12 then what are its direction cosines?​

  • Question 14
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    The direction cosines of the line equally inclined with the axes, are:​

  • Question 15
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    If a line makes angles 45 °,150 °, 135 °, with x, y and z-axes respectively, find its direction cosines.

  • Question 16
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    Find the equation of the set of points which are equidistant from the points (1, 2 , 3) and (3, 2, -1)​

  • Question 17
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    If a line in the ZX-plane makes an angle 60o with Z-axis, the direction cosines of this line are:

  • Question 18
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    A line makes angles α, β, γwith the positive directions of X-axis, Y-axis and Z-axis, respectively, then the directions cosines of the line are:

  • Question 19
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    The signs of the X,Y and Z coordinates of a point that lies in the octant OXYZ ’is ​

  • Question 20
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    If a line in the ZX-plane makes an angle 30o with Z-axis, the direction cosines of this line are:

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