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Math Exercises: Vectors

 

 

 

 

1. Find the length of a line segment and the coordinates of its midpoint. Draw the line segment in the coordinate system :

 

Vectors - Exercise 1

 

2. Find the coordinates of a vector given by two points and calculate the size of a vector. Draw a vector in the coordinate system :

 

Vectors - Exercise 2

 

3. Find the coordinates of vectors –v, 2v, –2.5v and draw the vectors in the coordinate system, if :

 

Vectors - Exercise 3

 

4. Find out whether the given vectors are linearly dependent (collinear). If so, find the coefficient of collinearity k :

 

Vectors - Exercise 4

 

5. Consider three vectors u = (–1;5), v = (2.7;3.8), w = (4.2;–6). Find the coordinates of vectors :

 

Vectors - Exercise 5

 

6. Find the scalar product of vectors :

 

Vectors - Exercise 6

 

7. Find the size of the angle between vectors :

 

Vectors - Exercise 7

 

8. Find out whether the given vectors are perpendicular to each other :

 

Vectors - Exercise 8

 

9. Consider two vectors u = (3;–2), v = (–1;b). Determine the parameter b so that :

 

Vectors - Exercise 9

 

10. Find the vector u that is perpendicular to the vector v = (3;4) and the size of which is 15.

 

11. Prove that the triangle ABC, A [16;1;–2], B [–9;1;–2], C [0;1;10], is right-angled. Find its perimeter, area and the size of its internal angles.

 

12. Consider three points A [0;1;2], B [1;2;0], C [2;0;1].


a) Prove that the points A, B, C form a triangle.
b) Find the size of the internal angle α.
c) Find the length of the median of side a and the coordinates of the centroid T.
d) Find the perimeter of the triangle ABC.
e) Find the area of the triangle ABC.

 

 

 

 

 

 

You might be also interested in:

- Straight Lines and Planes

- Relative Positions of Lines and Planes

- Conic Sections

- Matrices

 

 
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