Question

If \(\vec{a} = \vec{i} - \vec{j} + \vec{k}\) and \(\vec{b} = 2\vec{i} + \vec{j} + 3\vec{k}\), then find the value of \(|\vec{a} + \vec{b}|\).

Hint:

To find the magnitude of vector sum, add corresponding components and then apply the formula \(\sqrt{x^2 + y^2 + z^2}\).

Answer 1

Calculate \(\vec{a} + \vec{b}\): \[ \vec{a} + \vec{b} = (1 + 2)\vec{i} + (-1 + 1)\vec{j} + (1 + 3)\vec{k} = 3\vec{i} + 0\vec{j} + 4\vec{k}. \] Magnitude: \[ |\vec{a} + \vec{b}| = \sqrt{3^2 + 0^2 + 4^2} = \sqrt{9 + 0 + 16} = \sqrt{25} = 5. \]
Final answer: \[ \boxed{ 5. } \]