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Introduction to Three Dimensional Geometry

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2 months ago

Introduction to Three Dimensional Geometry Maths NCERT Exemplar Solutions Class 11th Chapter Twelve

The three coordinate planes divide the space into ____ parts.

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Payal Gupta

Contributor-Level 10

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} E i g h t . \\ H e n c e, t h e v a l u e o f t h e f i l l e r i s e i g h t . \end{array}$

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New answer posted

2 months ago

Introduction to Three Dimensional Geometry Maths NCERT Exemplar Solutions Class 11th Chapter Twelve

Match each item given under Column C₁ to its correct answer given under Column C₂:

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Payal Gupta

Contributor-Level 10

This is a matching answer type question as classified in NCERT Exemplar

$\begin{array}{l} (a) I n x y - p l a n e, z - c o o r d i n a t e i s z e r o . \\ H e n c e, (a) \leftrightarrow (i i i) . \\ (b) T h e point (2, 3, 4) l i e s i n f i r s t octant . \\ H e n c e, (b) \leftrightarrow (i) . \\ (c) L o c u s o f t h e points w i t h x - c o o r d i n a t e i s z e r o i s y z - p l a n e . \\ H e n c e, (c) \leftrightarrow (i i) . \\ (d) A l i n e i s p a r a l l e l t o x - a x i s i f a n d o n l y i f a l l t h e points o n t h e l i n e \\ h a v e e q u a l y a n d z - c o o r d i n a t e s . \\ H e n c e, (d) \leftrightarrow (v i) . \\ (e) x = 0, y = 0 r e p r e s e n t s z - a x i s . \\ H e n c e, (e) \leftrightarrow (i v) . \\ (f) z = c r e p r e s e n t a p l a n e p a r a l l e l t o x y - p l a n e . \\ H e n c e, (f) \leftrightarrow (v) . \\ (g) T h e p l a n e s x = a, y = b r e p r e s e n t t h e l i n e p a r a l l e l t o z - a x i s . \\ H e n c e, (g) \leftrightarrow (v i i i) . \\ (h) C o o r d i n a t e s o f a point a r e t h e distances f r o m t h e o r i g i n t o t h e f e e t o f p e r p e n d i c u l a r f r o m \\ t h e point o n t h e r e s p e c t i v e a x e s, \\ H e n c e, (h) \leftrightarrow (v i i) . \\ (i) A b a l l i s s o l i d r e g i o n i n t h e s p a c e e n c l o s e d b y a s p h e r e . \\ H e n c e, (i) \leftrightarrow (x) . \\ (j) T h e r e g i o n i n t h e p l a n e e n c l o s e d b y a c i r c l e i s k n o w n a s a d i s c . \\ H e n c e, (i) \leftrightarrow (i x) . \end{array}$

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New answer posted

2 months ago

Introduction to Three Dimensional Geometry Maths NCERT Exemplar Solutions Class 11th Chapter Twelve

The coordinates of a point are the perpendicular distances from the ____ on the respective axes.

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Payal Gupta

Contributor-Level 10

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} G i v e npoints \\ H e n c e, t h e v a l u e o f t h e f i l l e r i s g i v e n . \end{array}$

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New answer posted

2 months ago

Introduction to Three Dimensional Geometry Maths NCERT Exemplar Solutions Class 11th Chapter Twelve

The three planes determine a rectangular parallelepiped which has ____ rectangular faces.

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Payal Gupta

Contributor-Level 10

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h r e e p a i r s . \\ H e n c e, t h e v a l u e o f t h e f i l l e r i s t h r e e p a i r s . \end{array}$

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New answer posted

2 months ago

Introduction to Three Dimensional Geometry Maths NCERT Exemplar Solutions Class 11th Chapter Twelve

The three axes $O X, O Y, O Z$ determine ____.

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Payal Gupta

Contributor-Level 10

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h e t h r e e a x e s O X, O Y a n d O Z determine t h r e e c o o r d i n a t e p l a n e s . \\ H e n c e, t h e f i l l e r v a l u e i s t h r e e c o o r d i n a t e p l a n e s . \end{array}$

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New answer posted

2 months ago

Introduction to Three Dimensional Geometry Maths NCERT Exemplar Solutions Class 11th Chapter Twelve

$L$ is the foot of the perpendicular drawn from a point $(3, 4, 5)$ on the $x$ -axis. The coordinates of $L$ are

(a) $(3, 0, 0)$

(b) $(0, 4, 0)$

(c) $(0, 0, 5)$

(d) None of these

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Payal Gupta

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} W e k n o w t h a t o n x - a x i s, y = 0 a n d z = 0 . \\ S o, t h e r e q u i r e d c o o r d i n a t e s a r e (3, 0, 0) . \\ H e n c e, t h e c o r r e c t o p t i o n i s (a) . \end{array}$

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New answer posted

2 months ago

Introduction to Three Dimensional Geometry Maths NCERT Exemplar Solutions Class 11th Chapter Twelve

$L$ is the foot of the perpendicular drawn from a point $P (3, 4, 5)$ on the $x y$ -plane. The coordinates of point $L$ are

(a) $(3, 0, 0)$

(b) $(0, 4, 5)$

(c) $(3, 0, 5)$

(d) None of these

0 Follower 2 Views

Payal Gupta

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} W e k n o w t h a t o n x y p l a n e, z = 0 \\ S o, t h e c o o r d i n a t e s o f t h e point L a r e (3, 4, 0) . \\ H e n c e, t h e c o r r e c t o p t i o n i s (d) . \end{array}$

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New answer posted

2 months ago

Introduction to Three Dimensional Geometry Maths NCERT Exemplar Solutions Class 11th Chapter Twelve

If a parallelepiped is formed by planes drawn through the points $(5, 8, 10)$ and $(3, 6, 8)$ parallel to the coordinate planes, then the length of the diagonal of the parallelepiped is

(a) $2 \sqrt[]{3}$

(b) $3 \sqrt[]{2}$

(c) $\sqrt[]{2}$

(d) $\sqrt[]{3}$

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Payal Gupta

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} G i v e n points a r e A (5, 8, 10) a n d B (3, 6, 8) \\ ∴ A B = \sqrt[]{{(5 - 3)}^{2} + {(8 - 6)}^{2} + {(10 - 8)}^{2}} = \sqrt[]{4 + 4 + 4} = \sqrt[]{12} = 2 \sqrt[]{3} \\ H e n c e, t h e c o r r e c t o p t i o n i s (a) . \end{array}$

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New answer posted

2 months ago

Introduction to Three Dimensional Geometry Maths NCERT Exemplar Solutions Class 11th Chapter Twelve

The locus of a point for which $x = 0$ is

(a) $x y$ -plane

(b) $y z$ -plane

(c) $z x$ -plane

(d) None of these

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Payal Gupta

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} O n t h e y z p l a n e, x = 0 \\ H e n c e, t h e l o c u s o f t h e point i s y z p l a n e . \\ H e n c e, t h e c o r r e c t o p t i o n i s (b) . \end{array}$

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New answer posted

2 months ago

Introduction to Three Dimensional Geometry Maths NCERT Exemplar Solutions Class 11th Chapter Twelve

The locus of a point for which $y = 0, z = 0$ is

(a) Equation of x-axis

(b) Equation of y-axis

(c) Equation of z-axis

(d) None of these

0 Follower 3 Views

Payal Gupta

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} W e k n o w t h a t o n e e q u a t i o n o f x a x i s, y = 0, z = 0 \\ H e n c e, t h e l o c u s o f t h e point i s e q u a t i o n o f x a x i s . \\ H e n c e, t h e c o r r e c t o p t i o n i s (a) . \end{array}$

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