Math Exercises: Vectors
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].
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