Math topic中文

Position vectors

position vectors

Practice questions

  1. 1In the diagram, OA→=6a\overrightarrow{OA} = 6a, OB→=6b\overrightarrow{OB} = 6b and 3AN→=AB→3\overrightarrow{AN} = \overrightarrow{AB}.…
  2. 2In the diagram, OABC is a parallelogram and D is the midpoint of BC. BE and OC produced intersect at point F. It is give…
  3. 3ABCD is a parallelogram. A is the point (−6,−2)(-6,-2) and B is the point (−4,−7)(-4,-7). BC→=(8−2)\overrightarrow{BC} = \begin{pmatrix}8\\-2\end{pmatrix}…
  4. 4It is given that PQ→=(−56)\overrightarrow{PQ}=\begin{pmatrix}-5\\6\end{pmatrix} and the position vector of PP is (2−4)\begin{pmatrix}2\\-4\end{pmatrix}…
  5. 5CBEO is a parallelogram. The position vectors of C and E, relative to O, are a\mathbf{a} and b\mathbf{b} respectively.…
  6. 6A is the point (2,3) and B is the point (3,-5). Find the equation of the line AB. Answer ... Find the length of AB. Answ…
  7. 7AB‾=(71)\overline{AB} = \begin{pmatrix}7\\1\end{pmatrix}. D is the point (−2,1)(-2,1) and E is (h,6)(h,6). Express DE→\overrightarrow{DE}…
  8. 8OABD is a parallelogram. O is the origin. A is the point (-7, 3) and AB→=(412)\overrightarrow{AB}=\begin{pmatrix}4\\12\end{pmatrix}…
  9. 9OBC, ADC, AEB and OED are straight lines. OA→=a\overrightarrow{OA}=a and OB→=b\overrightarrow{OB}=b. OB=13OCOB=\dfrac{1}{3}OC, AE:EB=3:2AE:EB=3:2…
  10. 10It is given that AB→=(−12a)\overrightarrow{AB}=\begin{pmatrix}-12\\a\end{pmatrix}, a>0a>0 and ∣BA→∣=37|\overrightarrow{BA}|=37 units. F…
  11. 11The position vector of A is (34)\begin{pmatrix}3\\4\end{pmatrix} and the position vector of B is (710)\begin{pmatrix}7\\10\end{pmatrix}…
  12. 12The triangle with vertices A (2, 5), B (−2, −3) and C (2, −2) is shown in the diagram below. Find (a) the area of triang…
  13. 13ORS is a triangle. J is a point on RS such that RJ:JS=3:2RJ:JS = 3:2. OR→=r\overrightarrow{OR} = r and OS→=s\overrightarrow{OS} = s.…
  14. 14The position vector of point X is (8−4)\begin{pmatrix}8\\-4\end{pmatrix}. The position vector of point Y is (64)\begin{pmatrix}6\\4\end{pmatrix}…
  15. 15In the diagram, OA→=a\overrightarrow{OA} = a and OB→=b\overrightarrow{OB} = b. 2OB→=3BC→,  OD→=3OA→,  and 2AX→=XB→.2\overrightarrow{OB} = 3\overrightarrow{BC},\; \overrightarrow{OD} = 3\overrightarrow{OA},\; \text{and } 2\overrightarrow{AX} = \overrightarrow{XB}.…
  16. 16PQR is a triangle. PQ→=(2−3)\overrightarrow{PQ}=\begin{pmatrix}2\\-3\end{pmatrix}, PR→=(−39)\overrightarrow{PR}=\begin{pmatrix}-3\\9\end{pmatrix}…
  17. 17The point A is (0,7) and the point B is (6,9). Express AB→\overrightarrow{AB} as a column vector. The equation of AB is x…
  18. 18The position vector of point Q is (−7−3)\begin{pmatrix}-7\\-3\end{pmatrix} and the position vector of point R is (51)\begin{pmatrix}5\\1\end{pmatrix}…
  19. 19The figure shows a triangle ABC. E is the mid-point of AC. AB‾=3a\overline{AB}=3a and AC‾=3c\overline{AC}=3c. K lies on EB such…
  20. 20The figure shows a rectangle ABCD with AD = 15 cm. E is on DC produced such that DE = 8 cm. The area of shaded part X is…
  21. 21The points A, B and C have coordinates (1, 0), (3, 7) and (3, 5) respectively. Find ∠BAC\angle BAC. Answer ___
  22. 22Given that the coordinates of A is (2, -3), AB→=(−57)\overrightarrow{AB}=\begin{pmatrix}-5\\7\end{pmatrix} and FE→=k(2.5−3.5)\overrightarrow{FE}=k\begin{pmatrix}2.5\\-3.5\end{pmatrix}…
  23. 23Point A is translated to point B by the vector (−54)\begin{pmatrix}-5\\4\end{pmatrix}. The position vector of point B is (38)\begin{pmatrix}3\\8\end{pmatrix}…
  24. 24The position vectors of points A and B are (−93)\begin{pmatrix}-9\\3\end{pmatrix} and (1−12)\begin{pmatrix}1\\-12\end{pmatrix}…
  25. 25C is the point (−9,1)(-9,1) and D is the point (7,4)(7,4). CE→=(−28).\overrightarrow{CE} = \begin{pmatrix} -2 \\ 8 \end{pmatrix}. Calcu…
  26. 26A, B, C and D are four points such that the coordinates of A and C are (4,2) and (10,−34) respectively. AB→=(−9−12)\overrightarrow{AB}=\begin{pmatrix}-9\\-12\end{pmatrix}…