Question

6. An equilateral triangle with vertices A, B, C is inscribed in a circle with center O Thus we have vectors a OA, b OB, c O (a) Compute the sum a+b+c. (Hint: compute the scalar product of a+b+c with itself.) give a physical answer in (a).

Answer 1

"Given OA^rightarrow = a OB^rightarrow = 6 OC^rightarrow = C Assume side of an equilateral triangle to be P then, An Altitude from a vertex to a side in an equilateral triangle divides it in two equal parts \r\n AD = squareroot P^2 - P^2/r = squareroot 3P^2/4 = squareroot 3P/2 Now the point 0 where three altitudes melt divides altitude as following A0 = 2/3 of AD = 2/3 times squareroot 3 P/2 = p/squareroot 3 a = b = c = P/squareroot 3 \r\n a + b + c = P/squareroot 3 + P/squareroot 3 + P/squareroot 3 = 3 times P/squareroot 3 = P Squareroot 3 resultant of OB^rightarrow and OC^rightarrow will be equal to the magnitude of and will be perpendicularly downward in direction opposite to that of OA^rightarrow So net F^rightarrow =