Question 1219

Vectors I: Basics, Dot and Cross Products

2019 Paper 2 Question 5 Variant

Question

With reference to the origin

{O, }

the points

{A,B,C }

and

{D}

are such that

{\overrightarrow{OA}=\mathbf{a}, }

{\overrightarrow{OB}=\mathbf{b}, }

{\overrightarrow{OC}=3 \mathbf{a} + 2 \mathbf{b} }

and

{\overrightarrow{OD}=\mathbf{b} + 4 \mathbf{a}.}

The lines

{BD}

and

{AC}

cross at

{X.}

(i)

Express

{\overrightarrow{OX}}

in terms of

{\mathbf{a}}

and

{\mathbf{b}.}

[4]

The point

{Y}

lies on

{CD}

and is such that the points

{O,X }

and

{Y}

are collinear.

(ii)

Express

{OY}

in terms of

{\mathbf{a}}

and

{\mathbf{b}}

and find the ratio

{OX:OY.}

[6]

Answer

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