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A. Types of Projection

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  1. B. Using Projection in Calculations
  2. Ex. 6.1 Listen to the text and define types of companies.
  3. Examples of Projection Using the Units and Products
  4. F. Area of Projection of a Figure
  5. FEES AND ENROLMENT TYPES
  6. Finding the Distance Between Two Skew Lines by Projection

1. DABC is a triangle in a plane and DA1B1C1 is its projection in another plane. Given that AA1 = 6 cm, BB1 = 9 cm and CC1 = 12 cm. Find the distance between the centroids of these triangles.

2. Two intersecting planes α and b are given. Line d is their intersection. Given that a line n is perpendicular to α and line m is parallel to n. What can we say about m and d?

3. An equilateral triangle DABC is given in a plane α.

a. Can we always say that its projection is also an equilateral triangle?

b. If plane b is passing through AB then can we say that projection of DABC on b is equilateral?

c. At which condition the projection of DABC in plane b is an equilateral triangle?

4. ABCD is a square in plane α. Plane b passes through AB. The distance between the intersection point of diagonals of ABCD and plane b is 7 cm. Find the distance between point D and plane b.

5. Given that AB and CD are two line segments in space. Both of AB and CD are parallel to line d. Distance between AB and d is 12 cm, CD and d is 6 cm. If both of the lengths of AB and CD are 20 cm and length of projection of AB in line d is 10 cm find the length of the projection of line CD in d?

6. An isosceles right triangle has legs 12 cm. The hypothenuse of this triangle is parallel to a line d. What is the length of the projection of this triangle in line d?

 

7. Can we say that the projection of a right angle in a plane is also a right angle if none of the arms of the angle are parallel to given plane?

8. In the figure the lines d1 and d2 are perpendicular to each other. The projection of point S on the plane of lines d1 and d2 is point A. The points K, L, M and N are equidistant from A. Given that,

KM = 24 cm and KS = 13 cm.

Find A(DKNS) + A(DKMS).

 

9. In the figure G is centroid of equailateral triangle DABC. R is an exterior point and RG (ABC). Given that,

AB = 12 cm and

RG = 4 cm.

Find RC.

 

10. In the figure the planes P and Q intersected alond the line d. Point A is in plane P and AB d. T is the projection of point A in plane Q. Given that,

AT = 4 cm,

TB = 3 cm and

BC = 5 cm.

Find AC.

 

11. In the figure the lines d1, d2, d3 are perpendicular to the parallel planes P and T. The three lines are equidistant from each other. Distance between the planes P and T is 16 cm.

If R is the midpoint of AK and AK = find the distance from S to R.

 


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Читайте в этой же книге: Алматы 2013 г. | Проблема:What are the new challenges for MULTILINGUALISM IN EUROPE? | Identify the key problems and challenges with the contemporary mode of global governance. | I. Projection of a Point on a Line | Iii. Projection of a Figure on a Plane | A. Angle Between Two Lines | Check Yourself 13 | D. Polyhedral Angles | Check Yourself 14 | F. Area of Projection of a Figure |
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