I tried using trigonometry and using vectors. I can't get proper relations . I got |a|=|b| but can't proceed any further. Please help
2026-04-02 10:42:16.1775126536
Vectors angle between two lines
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Hints: The condition $\ \overline b\cdot(\overline a +\overline c)= \overline b \cdot \overline b + \overline a \cdot\overline c\ $ implies $$ (\overline b-\overline c)\cdot(\overline a-\overline b)=0\ . $$ That is, the side $\ CB\ $ is perpendicular to the side $\ BA\ $. Thus, $\ ABC\ $ is a right-angled triangle (with the right angle at $\ B\ $), and sides $\ AB\ $ and $\ BC\ $ of lengths $3$ and $4$ respectively.
The points $\ M\ $ and $\ D\ $ are the midpoints of sides $\ BC\ $ and $\ AC\ $ respectively, so what can you say about the relation between the triangles $\ DMC\ $ and $\ ABC\ $. Can you use this relation to deduce the length of $\ DM\ $? As usual, a well-drawn diagram should be extremely useful in solving the problem.