Exercises
In this problem set, we will use angle brackets to denote points, e.g. \(\point{1\\0},\) and square brackets to denote vectors, e.g. \(\vector{3\\2}.\) This is not standard notation. Typically both are denoted by square brackets (or parentheses), and distinguished by context (if at all).
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Compute the following expressions if they make sense, or answer "meaningless" if they do not make sense.
- \(\point{1\\2} - \point{2\\1}\)
- \(\point{-1\\\tfrac12} + \vector{1\\\tfrac32}\)
- \(\point{1\\0} + \point{0\\1}\)
- \(\vector{-3\\1} + \vector{2\\2}\)
- \(\vector{1\\1\\1} + \vector{2\\1}\)
- \(2\vector{1\\\tfrac12}\)
- \(2\point{1\\\tfrac12}\)
- \(2\vector{1\\\tfrac32\\-1} - \vector{0\\\tfrac12\\-1}\)