A force vector applied on a mass is represented as $\vec{F} = 3\hat{i} - 4\hat{j} + 12\hat{k}$ and a

Question

A force vector applied on a mass is represented as $\vec{F} = 3\hat{i} - 4\hat{j} + 12\hat{k}$ and accelerates it with $2 \mathrm{~m} / \mathrm{s}^{2}$. What will be the mass of the body?

Professor PC Thomas Classes · Answer

Magnitude of force $|\vec{F}| = \sqrt{3^2 + (-4)^2 + 12^2} = \sqrt{9 + 16 + 144} = \sqrt{169} = 13 \mathrm{~N}$. Acceleration $a = 2 \mathrm{~m/s}^2$. Mass $m = |\vec{F}| / a = 13 / 2 = 6.5 \mathrm{~kg}$.