1.Define a unit vector. What is its magnitude and physical purpose?
Sol: A unit vector has magnitude $1$ and specifies direction. $\hat{A} = \frac{\vec{A}}{|\vec{A}|}$.
2.State the triangle law of vector addition.
Sol: If two vectors are represented in magnitude and direction by two sides of a triangle taken in order, their resultant is given by the third side taken in reverse order.
3.What is the dot product of two perpendicular vectors?
Sol: Zero, because $\cos 90^\circ = 0$.
4.Calculate the magnitude of $\vec{A} = 3\hat{i} + 4\hat{j} + 12\hat{k}$.
Sol: $|\vec{A}| = \sqrt{3^2 + 4^2 + 12^2} = \sqrt{9 + 16 + 144} = \sqrt{169} = 13$.
