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, 2v, –2.5v and draw the vectors in the coordinate system, if :

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

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

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), v = (–1;b). Determine the parameter b so that :

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

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.

You might be also interested in: