Hits: 839

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#6

Hits: 839 Question In the diagram, OABCDEFG is a cube in which each side has length 6. Unit vectors ,  and  are parallel to ,  and  respectively. The point  is such that   and the point  is the mid-point of . i.       Express each of the vectors  and  in terms of ,  and .    ii.       Find the angle OQP. Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/11) | Q#9

Hits: 257 Question Relative to an origin , the position vectors of the points ,  and  are given by and i.       Find angle AOB.    ii.       Find the vector which is in the same direction as  and has magnitude 30.   iii.       Find the value of the constant  for which  is perpendicular to . Solution i.   We recognize that  is angle […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | May-Jun | (P1-9709/01) | Q#6

Hits: 688 Question Relative to an origin , the position vectors of points  and  are given by i.      Find the value of  and hence state whether angle AOB is acute, obtuse or a right angle.    ii.       The point  is such that . Find the unit vector in the direction of OX. Solution i.   We recognize that  is angle between […]