Problem

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

Solution

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: \( ||v|| = \sqrt{169} \).

From Solvely APP
Source: https://solvelyapp.com/problems/8rk39Uni5s/

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