Question 1208

Vectors I: Basics, Dot and Cross Products
2008 Paper 1 Question 3 Variant

Question

Points O,A,B{O,A, B} are such that OA=3i4k{\overrightarrow{OA}=- 3 \mathbf{i} - 4 \mathbf{k}} and OB=2i5j+5k,{\overrightarrow{OB}=2 \mathbf{i} - 5 \mathbf{j} + 5 \mathbf{k}, } and the point P{P} is such that OAPB{OAPB} is a parallelogram.
(i)
Find OP.{\overrightarrow{OP}.}
[1]
(ii)
Find the size of angle AOB.{AOB.}
[3]
(iii)
Find the exact area of the parallelogram OAPB.{OAPB.}
[2]

Answer