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NCERT Class 12 Mathematics Chapters
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1.
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Distance of the point (p, q, r) from y-axis is :
(a) q (b) |q| (c) |q| + |r| (d)
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2.
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The coordinates of the foot of the perpendicular drawn from the point (2, – 3, 4) on the y-axis is
(a) (2, 3, 4) (b) (– 2, – 3, – 4) (c) (0, – 3, 0) (d) (2, 0, 4)
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3.
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The coordinates of the foot of the perpendicular drawn from the point (– 2, 8, 7) on the XZ-plane is
(a) (– 2, – 8, 7) (b) (2, 8, – 7) (c) (– 2, 0, 7) (d) (0, 8, 0)
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4.
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The length of the perpendicular drawn from the point (4, – 7, 3) on the y-axis is
(a) 3 units (b) 4 units (c) 5 units (d) 7 units
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5.
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The vector equation of XY-plane is
(a)
 (b)  (c)  (d)  |
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1.
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Find the coordinates of points on line
 which are at a distance of  units from origin.(CBSE 2023, 2M)
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2.
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If the equation of a line is 𝑥 = 𝑎𝑦 + 𝑏, 𝑧 = 𝑐𝑦 + 𝑑, then find the direction ratios of the line and a point on the line.
(CBSE 2023, 2M)
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3.
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Find the direction cosines of the line whose Cartesian equations are
5x - 3 = 15y + 7 = 3 - 10z.
(CBSE 2023, 2M)
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4.
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The equations of a line are 5x - 3 = 15y + 7 = 3 - 10z. Write the direction cosines of the line and find the coordinates of a point through which it passes.
(CBSE 2023, 2M)
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5.
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If a line makes an angle α, β, γ with the coordinate axes, then find the value of
cos2α + cos2β + cos2γ.
(CBSE 2022, 2M)
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Chapter Name
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Sub Topic Name
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Three Dimensional Geometry
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11.1 Introduction to Three-Dimensional Geometry
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11.2 Direction Cosines and Direction Ratios
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11.3 Equation of a Line in Space
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11.4 Equation of a Plane in Space
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11.5 Distance Between Two Points in Space
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11.6 Distance Between a Point and a Plane
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11.7 Angle Between Two Lines and Two Planes
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