Edexcel IGCSEAdditional MathematicsGeneral Applications7 Marks
The points A, B and C have position vectors a = beginpmatrix 2 1 3 endpmatrix, b = beginpmatrix 4 -1 5 endpmatrix and c = beginpmatrix k 3 1 endpmatrix respectively, relative to an origin O.
- (a)Find the vector vecAB.[2]
- (b)Given that vecAB is perpendicular to vecBC, find the value of the constant k.[5]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- M1 for b - a or beginpmatrix 4 -1 5 endpmatrix - beginpmatrix 2 1 3 endpmatrix
- A1 for beginpmatrix 2 -2 2 endpmatrix (cao)
- M1 for vecBC = c - b or beginpmatrix k 3 1 endpmatrix - beginpmatrix 4 -1 5 endpmatrix
- A1 for vecBC = beginpmatrix k-4 4 -4 endpmatrix
- M1 for setting vecAB · vecBC = 0
- A1 for 2(k-4) - 2(4) + 2(-4) = 0 (or equivalent)
- M1 for correctly solving their linear equation for k
- A1 for k=16 (cao)
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