WalesMathsQuick questions

AS Unit 1 Pure Mathematics A

Quick questions on Vectors in two dimensions: position vectors and ratios - WJEC A-Level Maths

5short 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 representing vectors?

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A vector in two dimensions can be written as a column

\begin{pmatrix} x \\ y \end{pmatrix}

or in unit-vector form

x\mathbf{i} + y\mathbf{j}

, where

\mathbf{i}

and

\mathbf{j}

point along the

x

- and

y

-axes. Two vectors are equal if they have the same components, regardless of where they are drawn.

What is dividing a segment in a ratio?

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To find the point

P

that divides

AB

in the ratio

m:n

, start at

A

and move the fraction

\dfrac{m}{m+n}

of the way along

\overrightarrow{AB}

What is q1?

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Find the magnitude of

\mathbf{v} = 5\mathbf{i} - 12\mathbf{j}

. [2 marks]

What is q2?

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Given

\mathbf{a} = 3\mathbf{i} + \mathbf{j}

and

\mathbf{b} = \mathbf{i} - 2\mathbf{j}

, find

2\mathbf{a} - \mathbf{b}

. [2 marks]

What is q3?

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M

is the midpoint of

AB

where

\mathbf{a} = 4\mathbf{i}

and

\mathbf{b} = 2\mathbf{i} + 6\mathbf{j}

. Find the position vector of

M

. [2 marks]

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