Edexcel IALMathematicsGeneral Applications11 Marks
Relative to a fixed origin O, the points A and B have position vectors a = beginpmatrix 2 3 -4 endpmatrix and b = beginpmatrix 4 -2 3 endpmatrix respectively.
- (a)Find the vector overrightarrowAB.[1]
- (b)Find the exact value of |overrightarrowAB|.[2]
- (c)The point C has position vector c = beginpmatrix 2 -1 5 endpmatrix. The line L₁ passes through A and C. Find a vector equation for L₁.[3]
- (d)The line L₂ has equation r = beginpmatrix 4 -2 3 endpmatrix + μ beginpmatrix 1 -1 2 endpmatrix. Show that L₁ and L₂ intersect and find the position vector of their point of intersection.[5]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- (a) B1: for overrightarrowAB = b - a or a - b.
- (b) M1: for using Pythagoras in 3D.
- (b) A1: for correct exact value.
- (c) B1: for direction vector.
- (c) M1: for using position vector of A or C with their direction vector.
- (c) A1: for correct equation.
- (d) M1: for setting components equal to form 3 equations.
- (d) M1: for solving any 2 equations for λ and μ.
- (d) A1: for showing consistency with the third equation.
- (d) M1: for substituting λ or μ into equation of line.
- (d) A1: for correct position vector.
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