The position vectors of A and B are (2i + j) and (-i + 4j) respectively; find |AB|.
Two fair dices, each numbered 1, 2, ..., 6, are tossed together. Find the probability that they both show even numbers.
Calculate, correct to the nearest degree, the angle between the vectors \(\begin{pmatrix} 13 \\ 1 \end{pmatrix}\) and \(\begin{pmatrix} 1 \\ 4 \end{pmatrix}\).
Simplify \(2\log_{3} 8 - 3\log_{3} 2\)
Evaluate \(\begin{pmatrix} 2 & 3 \\ 4 & 1 \end{pmatrix} \begin{pmatrix} 2 \\ 3 \end{pmatrix}\).
