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

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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 = [v_1, v_2, ..., v_n] ), then ( ||v|| = sqrt{v_1^2+ v_2^2 + ... + v_n^2} ).Step:2 ：Substituting the given values into the formula, we get ( ||v|| = sqrt{3^2+ (-4)^2 + 12^2} ).Step:3 ：Calculating the squares and the sum, we get ( ||v|| = sqrt{9+ 16 + 144} ).Step:4 ：Finally, computing the square root, we get ( ||v|| = sqrt{169} ).

Answer

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 = [v_1, v_2, ..., v_n] ), then ( ||v|| = sqrt{v_1^2+ v_2^2 + ... + v_n^2} ).Step: 2 ：Substituting the given values into the formula, we get ( ||v|| = sqrt{3^2+ (-4)^2 + 12^2} ).Step: 3 ：Calculating the squares and the sum, we get ( ||v|| = sqrt{9+ 16 + 144} ).Step: 4 ：Finally, computing the square root, we get ( ||v|| = sqrt{169} ).

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

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