Hits: 729

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/13) | Q#9

Hits: 729   Question The position vectors of points A and B relative to an origin O are given by and where  is a constant.      i.       In the case where OAB is a straight line, state the value of  and find the unit vector in the direction of .    ii.           In the case […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/12) | Q#7

Hits: 427   Question The position vectors of points A and B relative to an origin O are  and  are given by and where  is a constant.      i.       In the case where , calculate angle AOB.    ii.       Find the values of  for which  is a unit vector. Solution      i.   We are given that; In the case where , We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/11) | Q#9

Hits: 917 Question The position vectors of points A and B relative to an origin O are  and  respectively. The position vectors of points C and D relative to O are  and  respectively. It is given that and      i.       Find the unit vector in the direction of  .    ii.       The point E is the mid-point of CD. Find angle […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/13) | Q#2

Hits: 272 Relative to an origin , the position vectors of the points ,  and  are given by and Find     i.      the unit vector in the direction of , ii.   the value of the constant p for which angle . Solution i.   A vector in the direction of  is; Therefore, for the given case; A unit vector […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/12) | Q#8

Hits: 449   Question      i.       Find the angle between the vectors  and . The vector  has a magnitude of 15 units and is in the same direction as the vector . The vector  has a magnitude of 14 units and is in the same direction as the vector .    ii.       Express  and  in terms of ,  and .   iii.       Find […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/11) | Q#6

Hits: 347 Question Two vectors  and  are such that   and  , where  is a constant.      i.       Find the value of  for which  is perpendicular to .    ii.       For the case where , find the angle between the directions of  and  . Solution      i.   If  and  & , then  and  are perpendicular. Therefore, we need the […]