Vector in space
1. What are the properties of a vector in space.
Solution:
2.Find the length of segment AB, which has midpoint S at the origin of the coordinate axes and point A [6; -2; 3]
Solution:
The length of the line is |AB| = 14j
3.Determine the coordinates of vertex C [c1; c2; c3] in triangle ΔABC, if the vertices and centroid are at: A [3;3;3], B [-2;1;2], T [0;-1;0]. Also find the perimeter of this triangle.
Solution:
The perimeter of the triangle is approximately 29,6 j.
4.On the z-axis find the point that is equidistant from points A [ -2;1;4] and B [3;0;1]
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5. In the parallelepiped ABCDEFGH the coordinates of points A[2;-3;1], B[3;-4;2], D[4;2;-3], E[5;3;4] are known. Calculate the coordinates of the remaining points C, F, H, G
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6.Prove that triangle ΔABC is isosceles and right-angled if: A[2;-4;9], B[-1;-4;5], C[6;-4;6]
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7.Given the vectors:
Determine whether they are linearly dependent.
8.Determine whether the given four points lie in one plane. A[1;2;-1], B[0;1;5], C[-1;2;1], D[2;1;3]
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9.Calculate the area of triangle ΔABC whose vertices are at the points:
10.Calculate the volume of the quadrangular pyramid ABCDV, given its vertices: A[2;0;0], B[0;3;0], D[0;0;6], V[2;3;8]
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11. Determine the length of the median in triangle ABC, if A[1;0;2], B[-2;1;-3], C[0;-1;1].
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12. Determine the distance between the midpoints of segments AB and CD if:
13.Let A[1;2;8] and B[4;y;4], and |AB| = 5. What is y?
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14. Given points K, L, M, N. Calculate the coordinates of point N if:
15.Given points A[4;-3;2], B[5;0;-1]. Determine numbers m, n so that point C[2;m;n] lies on vector AB.
Please log in to view the solution.16.Determine the mutual position (relationship) of the vectors
17. Given three points in space A, B, C. Calculate the measure of the angle
18.Calculate the perimeter and area of triangle ABC, if its vertices are:
19. In triangle ABC the vertices A, B and centroid T are given. Determine the coordinates of vertex C if
20.Write vector u as a linear combination of vectors v and w if:
