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

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

Find the coordinates of vectors –* v*, 2

*, –2.5*

**v***and draw the vectors in the coordinate system, if :*

**v**

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

Consider three vectors * u = *(–1;5),

*(2.7;3.8),*

**v**=*(4.2;–6). Find the coordinates of vectors :*

**w**=

Find the scalar product of vectors :

Find the size of the angle between vectors :

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

Consider two vectors * u = *(3;–2),

*(–1;*

**v**=*b*). Determine the parameter

*b*so that :

Find the vector ** u** that is perpendicular to the vector

*(3;4) and the size of which is 15.*

**v**=

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.

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*.

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