Math topic中文

Collinearity

Collinearity.

Practice questions

1With reference to the origin $O$ , the points $A$ , $P$ and $Q$ have position vectors $\mathbf{a}$ , $\mathbf{p}$ and $\mathbf{q}$ …
2In the triangle shown below, one vertex is origin O, and the two other vertices are A and B where $\overrightarrow{OA}=\mathbf{a}$ …
3Referred to the origin $O$ , the points $A$ and $B$ are such that $\overrightarrow{OA}=\mathbf{a}$ and $\overrightarrow{OB}=\mathbf{b}$ …
4The position vectors of the points $A$ and $B$ relative to the origin $O$ are $\mathbf{a}$ and $\mathbf{b}$ respectively…
5Referred to the origin $O$ , the points $A$ and $B$ are such that $\overrightarrow{OA} = a$ and $\overrightarrow{OB} = b$ …
6Relative to the origin $O$ , points $A$ , $B$ and $C$ have position vectors $\mathbf{a}$ , $\mathbf{b}$ and $\mathbf{c}$ re…
7Relative to the origin $O$ , the points $A$ , $B$ , and $C$ have position vectors $\mathbf{a}$ , $\mathbf{b}$ and $3\mathbf{a}+\mathbf{b}$ …
8With reference to the origin $O$ , the points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ respectivel…
9To build a Virtual Reality (VR) experience, a virtual world is created to contain geometric models. With reference to th…
10With reference to the origin $O$ , the position vectors of points $A$ , $B$ and $C$ are expressed as $\overrightarrow{OA}$ …
11Relative to the origin O, points A and B have position vectors $\mathbf{a}$ and $\mathbf{b}$ respectively, where $\mathbf{a}$ …
12Relative to the origin $O$ , the points $A$ , $B$ , and $C$ have position vectors $\mathbf{a}$ , $\mathbf{b}$ and $3\mathbf{a}+\mathbf{b}$ …
13Referred to the origin O, let P, Q and R be distinct points with position vectors $\mathbf{p}$ , $\mathbf{q}$ and $\mathbf{r}$ …
14The above diagram shows a circle with radius $r$ units and centre $O$ . The points $A$ and $B$ on the circle are such tha…
15The position vector of point X is $\begin{pmatrix}8\\-4\end{pmatrix}$ . The position vector of point Y is $\begin{pmatrix}6\\4\end{pmatrix}$ …
166 equilateral triangles each with sides 5 units are arranged to form a regular hexagon as shown in the diagram below. By…
17With reference to the origin $O$ , the points $A$ , $B$ and $C$ are such that $\overrightarrow{OA} = \begin{pmatrix} 2 \\ 1 \\ -1 \end{pmatrix}$ …
18Referred to the origin O, let P, Q and R be distinct points with position vectors $\mathbf{p}$ , $\mathbf{q}$ and $\mathbf{r}$ …
19Relative to the origin $O$ , two fixed points, $A$ and $B$ , have position vectors $\mathbf{a}$ and $\mathbf{b}$ respectiv…
20The points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ respectively. $C$ is the point on line $OB$ s…
21若 $A(\text{-}2\text{,}3)$ ， $B(3\text{,-}2)$ ， $C(1\text{,}m)$ 三点共线，则 $m$ 的值为 $()$ A. $\text{-}2$ B. $\text{-}1$ C.…
22Referred to the origin $O$ , the points $A$ and $B$ are such that $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$ …
23The diagram shows a unit circle with centre $O$ and diameter $AB$ . The point $C$ lies on the circumference of the circle…
24As shown in the above parallelogram $OACB$ , $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$ . I…
25The points $P$ and $Q$ have position vectors $3\mathbf{i}+4\mathbf{j}-\mathbf{k}$ and $5\mathbf{i}+7\mathbf{j}+6\mathbf{k}$ …
26It is given that $\overrightarrow{OA} = 3\mathbf{i} + \mathbf{j} + 3\mathbf{k}$ and $\overrightarrow{OB} = 5\mathbf{i} - 4\mathbf{j} + 3\mathbf{k}$ …
27The points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ with respect to origin $O$ , where $\mathbf{a}$ …
28Referred to the origin $O$ , the points $A$ and $B$ are such that $\overrightarrow{OA}=\mathbf{a}$ and $\overrightarrow{OB}=\mathbf{b}$ …
29With respect to an origin $O$ , the points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ respectively w…
30With reference to the point $O$ as the origin and the x-y plane as a horizontal plane, the pyramid $OPQRV$ has a paralle…
31Referred to the origin $O$ , the position vectors of three points $A$ , $B$ and $P$ are $\mathbf{a}$ , $\mathbf{b}$ and $\mathbf{a} + 5\mathbf{b}$ …
32The position vectors of the points $A$ , $B$ and $C$ with respect to the origin $O$ are $\mathbf{a}$ , $\mathbf{b}$ and $\mathbf{c}$ …
33The points P, Q and R have position vectors p, q and r respectively, with respect to the origin O. The vector p is a uni…