Geometric proofs with vectors

12 questions

1. Work out the magnitude of the vector {4 \choose -3}.
2. Which of the following vectors are parallel to 2\mathbf{a}-3\mathbf{b}?
3. Which of the following vectors are parallel to {8\choose -12}?
4. X is a point on the line AB. Match each vector statement to the correct ratio.
5. Match each value of x to the vector equation that it satisfies.
6. OACB is a parallelogram. M is the midpoint of OA and N is the midpoint of OB. \overrightarrow{OM}=2\mathbf{a} and \overrightarrow{ON}=2\mathbf{b}.
7. Three points that lie along the same straight line are said to be ___.
8. Select the correct statements to show that ODEF is a trapezium.
9. Select the correct statements to show that OAEF is not a parallelogram.
10. ABCD is a kite. W,X,Y,Z are midpoints of the lines they lie on. \overrightarrow{XW} = k(\mathbf b - \mathbf a) where k= ___
11. ABCD is a kite. W,X,Y,Z are midpoints of the lines they lie on. Find \overrightarrow{ZW}.
12. ABCD is a kite. W,X,Y,Z are midpoints of the lines they lie on. Find \overrightarrow{XZ}.

License: OGL