Find the length of the vector \( \vec{v} = 3\hat{i} - 4\hat{j} + 2\hat{k} \)

Step 1 ：The formula to find the length or magnitude of a vector \( \vec{v} = a\hat{i} + b\hat{j} + c\hat{k} \) is given by \( \|v\| = \sqrt{a^2 + b^2 + c^2} \)

Step 2 ：Substitute the given values into the formula: \( \|v\| = \sqrt{3^2 + (-4)^2 + 2^2} \)

Step 3 ：Calculate the square of each component: \( \|v\| = \sqrt{9 + 16 + 4} \)

Step 4 ：Add the squared components: \( \|v\| = \sqrt{29} \)