I am attempting to help my daughter with her homework for Mechanics at the first year of A Level (AS) The question asks:
Given that vector a = 2i + 5j and vector b = 3i - j, find a) (lambda symbol) if a + lambda b is parallel to vector i
b) (mu symbol) if mu a + b is parallel to vector j
I have the solution to the problem from the CD supplied with the text book but I don't understand what the lambda symbol represents or the mu symbol. I have read the textbook and don't find any reference to what it means. Any explanations would be gratefully received. Thanks in advance.
Here $\lambda$ and $\mu$ are used as variables that stand for scale factors, in this case real numbers. That is, part a) asks what multiple of $\mathbf b$ needs to be added to $\mathbf a$ to make the resulting vector "parallel" to $\mathbf i$. (The answer to this part is $\lambda=5$, since $(2\mathbf i+5\mathbf j) + 5(3\mathbf i-\mathbf j)=17\mathbf i$.) Here "parallel" is not well expressed in the problem statement, since vectors are not lines that can be parallel; what they most likely mean is that the result is a multiple of $\mathbf i$.