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Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Commerce MCQ


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10 Questions MCQ Test Mathematics (Maths) Class 11 - Test: Introduction to Three Dimensional Geometry- Case Based Type Questions

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Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 1

ABCD is a parallelogram as shown in the figure. Three of its vertices are A(1, 2, 3), B(–1, –2, –1) and C(2, 3, 2).

Based on the above data, answer the following question.

Q. The fourth vertex D is ................

Detailed Solution for Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 1
Let D = (x, y, z)

Midpoint of AC = Midpoint of BD

i.e;

∴ D = (4, 7, 6)

Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 2

ABCD is a parallelogram as shown in the figure. Three of its vertices are A(1, 2, 3), B(–1, –2, –1) and C(2, 3, 2).

Based on the above data, answer the following question.

Q. Centroid of △BCD is ...............

Detailed Solution for Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 2

B = (–1, –2, –1)

C = (2, 3, 2)

D = (4, 7, 6)

Centroid of △BCD =

=

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Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 3

ABCD is a parallelogram as shown in the figure. Three of its vertices are A(1, 2, 3), B(–1, –2, –1) and C(2, 3, 2).

Based on the above data, answer the following question.

Q. Length of AB is .............. units.

Detailed Solution for Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 3

AB =

=

= √36

= 6 units

Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 4

ABCD is a parallelogram as shown in the figure. Three of its vertices are A(1, 2, 3), B(–1, –2, –1) and C(2, 3, 2).

Based on the above data, answer the following question.

Q. Length of BD is ........... units.

Detailed Solution for Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 4
B = (–1, –2, –1), D = (4, 7, 6)

BD =

=

= √155

Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 5

ABCD is a parallelogram as shown in the figure. Three of its vertices are A(1, 2, 3), B(–1, –2, –1) and C(2, 3, 2).

Based on the above data, answer the following question.

Q. Midpoint of AC is ...............

Detailed Solution for Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 5

Midpoint of AC =

=

Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 6

P is the point in space with coordinates (2,3,4) as shown in the diagram given below.

Based on the above data, answer the following question.

Q. Distance of P from the XZ plane is ............ units.

Detailed Solution for Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 6
Distance from XZ plane = |y| = 3 units
Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 7

P is the point in space with coordinates (2,3,4) as shown in the diagram given below.

Based on the above data, answer the following question.

Q. Midpoint of OP is ............

Detailed Solution for Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 7

Midpoint of OP =

=

Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 8

P is the point in space with coordinates (2,3,4) as shown in the diagram given below.

Based on the above data, answer the following question.

Q. Distance of P from x-axis is .......... units

Detailed Solution for Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 8

Distance from x-axis =

Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 9

P is the point in space with coordinates (2,3,4) as shown in the diagram given below.

Based on the above data, answer the following question.

Q. Foot of the perpendicular from P to the x-axis is ..............

Detailed Solution for Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 9
Foot of perpendicular to x-axis = (x, 0, 0) = (2, 0, 0)
Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 10

P is the point in space with coordinates (2,3,4) as shown in the diagram given below.

Based on the above data, answer the following question.

Q. The point P is in .............. octant.

Detailed Solution for Test: Introduction to Three Dimensional Geometry- Case Based Type Questions - Question 10
The point P is in I octant.
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