If \( n \) is an integer and \( Z = \cos \theta + i \sin \theta, \theta \neq (2n + 1)\frac{\pi}{2}, \) then: \[ \frac{1 + Z^{2n}}{1 - Z^{2n}} = ? \]
If \( L, M, N \) are the midpoints of the sides PQ, QR, and RP of triangle \( \Delta PQR \), then \( \overline{QM} + \overline{LN} + \overline{ML} + \overline{RN} - \overline{MN} - \overline{QL} = \):
Let a and b be two non-collinear vectors of unit modulus. If u = a − (a · b)b and v = a × b, then ∥v∥ = ?
If
and \( AA^T = I \), then \( \frac{a}{b} + \frac{b}{a} = \):
Find the shortest distance between the skew lines $\vec{r} = (-\hat{i} - 2\hat{j} - 3\hat{k}) + t(3\hat{i} - 2\hat{j} - 2\hat{k})$ and $\vec{r} = (7\hat{i} + 4\hat{k}) + s(\hat{i} - 2\hat{j} + 2\hat{k})$.