Hits: 252

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/13) | Q#7

Hits: 252   Question Three points, O, A and B, are such that  and  , where is a constant.      i. Find the values of  for which  is perpendicular to .    ii. The magnitudes of   and   are  and  respectively. Find the value of  for which .   iii. Find the unit vector in the direction of  when . Solution i.   We are given that; If  and […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#7

Hits: 1445   Question The diagram shows a pyramid OABCX. The horizontal square base OABC has side 8 units and the  centre of the base is D. The top of the pyramid, X, is vertically above D and XD = 10 units. The mid- point of OX is M. The unit vectors  and  are parallel to  and  respectively and the unit […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#6

Hits: 311   Question Relative to an origin O, the position vector of A is  and the position vector of B is  .      i.       Show that angle OAB is a right angle.    ii.       Find the area of triangle OAB. Solution i.   It is evident that angle OAB is the angle between vectors  and . We are given  but we need […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/13) | Q#7

Hits: 377 Question The position vectors of points A, B and C relative to an origin O are given by and i.       Show that angle .    ii.  Use the result in part (i) to find the exact value of the area of triangle ABC. Solution      i.   We recognize that angle BAC is between  and . Therefore, we need […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/12) | Q#7

Hits: 1402   Question The diagram shows a trapezium ABCD in which BA is parallel to CD. The position  vectors of A, B and C relative to an origin O are given by and      i.       Use a scalar product to show that AB is perpendicular to BC.    ii.       Given that the length of CD is 12 units, find […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#8

Hits: 366   Question Relative to an origin , the position vectors of the points  and  are given by and i.          Find the value of p for which angle  is . ii.       For the case where , find the unit vector in the direction of . Solution i.   We are given that angle  , hence,  and  are perpendicular […]