Using vectors prove that angle inscribed in a semi circle is a right angle
Asked by DIVYA GARG | 6th Jun, 2013, 01:36: PM
Expert Answer:
Center the circle at the origin, and scale to have radius 1. Let the vertex of the right triangle be at vector v, and let the diameter be the segment from the vector w to ?w.
Then (v?w)?(v?(?w))=(v?w)?(v+w)=(v?v)?(w?w)=1?1=0, so the angle formed by vw and v(?w) is a right angle.
Center the circle at the origin, and scale to have radius 1. Let the vertex of the right triangle be at vector v, and let the diameter be the segment from the vector w to ?w.
Then (v?w)?(v?(?w))=(v?w)?(v+w)=(v?v)?(w?w)=1?1=0, so the angle formed by vw and v(?w) is a right angle.
Answered by | 7th Jun, 2013, 01:37: AM
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