Dot Product


Drag the red dots to change the positions of A and B in the applet.
Exercises for students:
Solve the following and check your answers using the above applet:

Find the angle between the vectors 2i + 3j and 3i + j
Find the angle between the vectors -i + 3j and 3i + j
Find the angle between the vectors -3i - j and 3i + j
Find the angle between the vectors 6i + 2j and 3i + j


Show that the lines with equations r = 2i + t(i + 2j) and r = 4j + s(2i - j) are perpendicular.


Find the acute angle between the lines r = 2i + 3j + s(2i + 2j) and r = i + 2j + t(-3i + j), giving your answer correct to the nearest 0.1 degree.

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