Advanced problem solving with vectors

12 questions

1. Three points that lie along the ___________ are said to be collinear.
2. Select the correct statements to show that AEDB is a trapezium.
3. Select the correct statements to show that ABEF is a parallelogram.
4. ABCD is a kite. The midpoints of each side are shown. \overrightarrow{WX} = k(\mathbf a - \mathbf b) where k=___.
5. ABCD is a kite. W,X,Y,Z are midpoints of the lines they lie on. Find \overrightarrow{WZ}.
6. ABCD is a kite. W,X,Y,Z are midpoints of the lines they lie on. Find \overrightarrow{ZX}.
7. A ___ vector is the single vector that produces the same effect as a combination of other vectors.
8. Given \mathbf a = {2 \choose 3} and \mathbf b = {-1 \choose 2}, find 4\mathbf a - 2 \mathbf b
9. Given that x\choose 8 is parallel to 15 \choose 12, then x = ___
10. a {3\choose -2} + 4{ 3 \choose b} = {3\choose 14}. The value of b is ___
11. Given that a {2\choose 1} + b{ 4 \choose4}= {16 \choose 14}, find the value of a + b. a+b=___.
12. \mathbf a = {2\choose -3} and \mathbf b = {-2 \choose y}. Given that 3 \mathbf a - 2 \mathbf b is parallel to 30 \choose -51, the value of y is ___.

License: OGL