Find the resultant displacement when a vector of magnitude 5 units is added to a vector of magnitude 3 units at an angle of 45 degrees with regards to the x-axis.
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What is the result of adding the vector \[ \mathbf{a} = \begin{bmatrix} 3 \\ -2 \\ 4 \end{bmatrix} \]to the vector \[ \mathbf{b} = \begin{bmatrix} -1 \\ 5 \\ 2 \end{bmatrix} \]?
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How many tickets were sold if the total revenue from selling each ticket for $10 and $20 was $1500?