Question 1212

Vectors I: Basics, Dot and Cross Products
2012 Paper 1 Question 5 Variant

Question

Referred to the origin O,{O,} the points A{A} and B{B} have position vectors a{\mathbf{a}} and b{\mathbf{b}} such that
a=i2j2kandb=i+j.\begin{align*} \mathbf{a} &= \mathbf{i} - 2 \mathbf{j} - 2 \mathbf{k} \\ \textrm{and} \quad \mathbf{b} &= - \mathbf{i} + \mathbf{j}. \end{align*}
The point C{C} has position vector c{\mathbf{c}} given by c=λa+μb,{\mathbf{c}=\lambda \mathbf{a}+\mu \mathbf{b},} where λ{\lambda} and μ{\mu} are positive constants.
(i)
Given that the area of triangle OAC{OAC} is 92,{\frac{9}{2},} find μ.{\mu.}
[4]
(ii)
Given instead that μ=2{\mu = 2} and that OC=25,{OC = 2 \sqrt{5},} find the possible coordinates of C.{C.}
[4]

Answer