2.4: Exact magnitude, parallel condition and constants

0606/22/M/J/18 — Question 7 · 6 marks

Vectors i\mathbf{i} and j\mathbf{j} are vectors parallel to the xx-axis and yy-axis respectively.
Given that a=2i+3j\mathbf{a} = 2\mathbf{i} + 3\mathbf{j}, b=i−5j\mathbf{b} = \mathbf{i} - 5\mathbf{j} and c=3i+11j\mathbf{c} = 3\mathbf{i} + 11\mathbf{j}, find
(i)
the exact value of ∣a+c∣|\mathbf{a} + \mathbf{c}|,
[2]
(ii)
the value of the constant mm such that a+mb\mathbf{a} + m\mathbf{b} is parallel to j\mathbf{j},
[2]
(iii)
the value of the constant nn such that na−b=cn\mathbf{a} - \mathbf{b} = \mathbf{c}.
[2]