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Find the vector sum of three vectors vecA, vecB and vecC, using analytical method. |
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Answer» Solution :Let `vecA, vecB and vecC` be REPRESENTED in component from, `vecA=vecA_(x)hati+vecA_(y)hatj+vecA_(Z)hatk, vecB=vecB_(x)hati+vecB_(y)hatj+vecB_(z)hatk` `vecC=vecC_(x)hati+vecC_(y)hatj+vecC_(z)hatk` Let `vecD` be their SUMMATION vector, `vecD=(vecA+vecB+veccC)` `(vec(A_(x))hat(A_(y))hatj+vecA_(z)hatk)+(vec(B_(x))hati+vec(B_(y))hatj+vec(B_(z))hatk+vec(C_(x))hati+vec(C_(y))hatj+vec(C_(y))+vec(C_(z))hatk)` Addition of vecotrs obey the the commutative as well as associative laurs. `D=(A_(x)+B_(x)+C_(x))(2u sin theta)/(G)+(A_(y)+B_(y)+C_(y))hatj+(A_(z)+B_(z)+C_(z))hatk` `+(A_(x)+B_(x)+C_(x))hati+(A_(y)+B_(y)+C_(y))hatj+(A_(z)+B_(z)+C_(z))(2usintheta)/(g)` `D_(x)=A_(z)+B_(x)+C_(x), D_(y)=A_(y)+B_(y)+C_(y), D_(z)=A_(z)+B_(z)+C_(z)` |
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