Title: It is known that the midpoints of AB and AC on both sides of △ABC are M and N respectively. Take point P on the extension line of BN, so that NP=BN, and take point Q on the extension line of CM, so that MQ=CM. Prove the straight line of p, a, q * * with vector.

Test sites: parallel vector and * * * line vector.

Analysis: Take AB and AC on both sides of △ABC as vectors to construct a set of bases, construct two vectors from three points of the line to be proved, and express the vectors with bases. According to the triangle rule, two vector * * * lines are obtained. It is known that these two vector * * * lines have common points, so there are three * * * lines.

Answer:

Comments: In the process of solving problems in the future, it is very common to represent a vector with a set of vectors. The addition and subtraction of vectors is the basis of solving problems with vectors. Only by learning operation well can we use vectors to solve solid geometry problems and trigonometric functions. Many questions are based on vectors.

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