Problem

Find the norm of the vector v=[3,4,12] in real vector space.

Answer

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Answer

Finally, computing the square root, we get ||v||=169.

Steps

Step 1 :The norm of a vector v in real vector space is given by the square root of the sum of the squares of its components. In mathematical terms, if v=[v1,v2,...,vn], then ||v||=v12+v22+...+vn2.

Step 2 :Substituting the given values into the formula, we get ||v||=32+(4)2+122.

Step 3 :Calculating the squares and the sum, we get ||v||=9+16+144.

Step 4 :Finally, computing the square root, we get ||v||=169.

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