A-LevelMathematicsVectors9709/32 · Oct/Nov 2021 · Q1010 Marks
With respect to the origin O, the position vectors of the points A and B are given by OA = (1, 2, -1) and OB = (0, 3, 1).
- (a)Find a vector equation for the line l through A and B.[3]
- (b)The point C lies on l and is such that AC = 3AB. Find the position vector of C.[2]
- (c)Find the possible position vectors of the point P on l such that OP = √14.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [B1] Obtain direction vector -i+j+2k, or equivalent
- [M1] Use a correct method to form a vector equation
- [A1] State answer r = i + 2j − k + λ (− i + j + 2k), or equivalent correct form
- [M1] Use a correct method to find the position vector of C
- [A1] Obtain answer 2i + 5j +5k, or equivalent
- [B1 FT] State OP in component form
- [M1] Form an equation in λ by equating the modulus of OP to √14, or equivalent
- [A1] Simplify and obtain 3λ² – λ− 4 = 0, or equivalent
- [M1] Solve a 3-term quadratic and find a position vector
- [A1] Obtain answers 2i + j – 3k and −1/3 i + 10/3 j + 5/3 k, or equivalent
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