Find the length of the vector (v = (4, 3, 12)).

Question

Accepted Answer

Step:1 ：We are given the vector ( v = (4, 3, 12) ). The length (or magnitude) of a vector (v = (a, b, c)) in three-dimensional space is given by the formula ( ||v|| = sqrt{a^2 + b^2 + c^2} ).Step:2 ：Substitute the values into the formula: ( ||v|| = sqrt{4^2 + 3^2 + 12^2} ).Step:3 ：Solve the equation: ( ||v|| = sqrt{16 + 9 + 144} ).Step:4 ：Simplify the equation: ( ||v|| = sqrt{169} ).

Answer

Step: 1 ：We are given the vector ( v = (4, 3, 12) ). The length (or magnitude) of a vector (v = (a, b, c)) in three-dimensional space is given by the formula ( ||v|| = sqrt{a^2 + b^2 + c^2} ).Step: 2 ：Substitute the values into the formula: ( ||v|| = sqrt{4^2 + 3^2 + 12^2} ).Step: 3 ：Solve the equation: ( ||v|| = sqrt{16 + 9 + 144} ).Step: 4 ：Simplify the equation: ( ||v|| = sqrt{169} ).

Find the length of the vector \(v = (4, 3, 12)\).

Answer

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