Learn Maths Three Dimensional Geometry, Class 12 Maths Three Dimensional Geometry Exercise, Free Online Three Dimensional Geometry Lessons

Class 12 Maths Study Material

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Three Dimensional Geometry

Which of the following set of points are non-collinear?

a) (1, -1, 1), (-1, 1, 1), (0, 0, 1)
b) (1, 2, 3), (3, 2, 1), (2, 2, 2)
c) (-2, 4, -3), (4, -3, -2), (-3, -2, 4)
d) (2, 0, -1), (3, 2, -2), (5, 6, -4)

✔Answer

Correct Answer Is : (-2, 4, -3), (4, -3, -2), (-3, -2, 4)

Solution Is :

If O is the origin and OP = 3 with direction ratios -1, 2, -2, then co-ordinates of P are?

a) (1, 2, 2)
b) (-1, 2, -2)
c) (-3, 6, -9)
d) (-1/3, 2/3, -2/3)

✔Answer

Correct Answer Is : (-1, 2, -2)

Solution Is :

If 1/2, 1/3, n are direction cosines of a line, then the value of n is?

a) √(23)/6
b) 23/6
c) 2? 3
d) 1? 6

✔Answer

Correct Answer Is : √(23)/6

Solution Is :

If the co-ordinates of A and B be (1, 2, 3) and (7, 8, 7), then the projections of the line segment AB on the co-ordinate axes are?

a) 4, 6, 4
b) 3, 3, 2
c) 6, 6, 4
d) 2, 3, 2

✔Answer

Correct Answer Is : 6, 6, 4

Solution Is :

The projection of the line joining the points (3, 4, 5) and (4, 6, 3) on the line joining the points (-1, 2, 4) and (1, 0, 5), is?

a) 4/3
b) 2? 3
c) 1? 3
d) 1? 2

✔Answer

Correct Answer Is : 4/3

Solution Is :

The straight line (x - 3)/3 = (y - 2)/1 = (z - 1)/0 is?

a) Parallel to X-axis
b) Parallel to Y-axis
c) Parallel to Z-axis
d) Perpendicular to Z-axis

✔Answer

Correct Answer Is : Perpendicular to Z-axis

Solution Is :

The equation of the line passing through the points (3, 2, 4) and (4, 5, 2) is?

a) (x + 3)/1 = (y + 2)/3 = (z + 4)/-2
b) (x - 3)/1 = (y - 2)/3 = (z - 4)/-2
c) (x + 3)/7 = (y + 2)/7 = (z + 4)/6
d) (x - 3)/7 = (y - 2)/7 = (z - 4)/6

✔Answer

Correct Answer Is : (x - 3)/1 = (y - 2)/3 = (z - 4)/-2

Solution Is :

If (x - 1)/l = (y - 2)/m = (z + 1)/n is the equation of the line through (1, 2, -1) and (-1, 0, 1), then (l, m, n) is?

a) (-1, 0, 1)
b) (1, 2, -1)
c) (1, 1, -1)
d) (0, 1, 0)

✔Answer

Correct Answer Is : (1, 1, -1)

Solution Is :

The line joining the points (-2, 1, -8) and (a, b, c) is parallel to the line whose direction ratios are 6, 2, 3. The value of a, b, c are?

a) 4, 3, -5
b) 1, 2, -13/2
c) 10, 5, -2
d) 4, 6, -5

✔Answer

Correct Answer Is : 4, 3, -5

Solution Is :

The perpendicular distance of the point (2, 4, -1) from the line (x + 5)/1 = (y + 3)/4 = (z - 6)/-9 is?

a) 9
b) 3
c) 5
d) 7

✔Answer

Correct Answer Is : 7

Solution Is :

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Class 12 Maths Study Material

Three Dimensional Geometry

Which of the following set of points are non-collinear?

Correct Answer Is : (-2, 4, -3), (4, -3, -2), (-3, -2, 4)

Solution Is :

If O is the origin and OP = 3 with direction ratios -1, 2, -2, then co-ordinates of P are?

Correct Answer Is : (-1, 2, -2)

Solution Is :

If 1/2, 1/3, n are direction cosines of a line, then the value of n is?

Correct Answer Is : √(23)/6

Solution Is :

If the co-ordinates of A and B be (1, 2, 3) and (7, 8, 7), then the projections of the line segment AB on the co-ordinate axes are?

Correct Answer Is : 6, 6, 4

Solution Is :

The projection of the line joining the points (3, 4, 5) and (4, 6, 3) on the line joining the points (-1, 2, 4) and (1, 0, 5), is?

Correct Answer Is : 4/3

Solution Is :

The straight line (x - 3)/3 = (y - 2)/1 = (z - 1)/0 is?

Correct Answer Is : Perpendicular to Z-axis

Solution Is :

The equation of the line passing through the points (3, 2, 4) and (4, 5, 2) is?

Correct Answer Is : (x - 3)/1 = (y - 2)/3 = (z - 4)/-2

Solution Is :

If (x - 1)/l = (y - 2)/m = (z + 1)/n is the equation of the line through (1, 2, -1) and (-1, 0, 1), then (l, m, n) is?

Correct Answer Is : (1, 1, -1)

Solution Is :

The line joining the points (-2, 1, -8) and (a, b, c) is parallel to the line whose direction ratios are 6, 2, 3. The value of a, b, c are?

Correct Answer Is : 4, 3, -5

Solution Is :

The perpendicular distance of the point (2, 4, -1) from the line (x + 5)/1 = (y + 3)/4 = (z - 6)/-9 is?

Correct Answer Is : 7

Solution Is :

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