SingaporeMathsQuick questions

Coordinate Geometry and Vectors

Quick questions on Vector geometry and position vectors explained: O-Level E-Maths

7short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are position vectors?

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The position vector of a point

A

relative to an origin

O

\overrightarrow{OA}

, often written

\mathbf{a}

. It locates the point as a displacement from the origin, and every point has its own position vector.

What are expressing a vector between two points?

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The vector from

A

B

is the end position vector minus the start:

What is the parallel condition?

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Two vectors are parallel when one is a scalar multiple of the other:

What is not following a connected route?

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Each step in a route must share a point with the next, joining nose to tail.

What is q1?

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Given

\overrightarrow{OA} = \mathbf{a}

and

\overrightarrow{OB} = \mathbf{b}

, write

\overrightarrow{AB}

in terms of

\mathbf{a}

and

\mathbf{b}

. [1 mark]

What is q2?

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\overrightarrow{PQ} = 2\overrightarrow{XY}

, what can you say about lines

PQ

and

XY

? [1 mark]

What is q3?

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M

is the midpoint of

AB

with position vectors

\mathbf{a}

and

\mathbf{b}

. Write

\overrightarrow{OM}

. [2 marks]

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