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Date	November 2018	Marks available	4	Reference code	18N.1.AHL.TZ0.H_5
Level	Additional Higher Level	Paper	Paper 1	Time zone	Time zone 0
Command term	Find and Hence or otherwise	Question number	H_5	Adapted from	N/A

Question

The vectors a and b are defined by a = $\left( {\begin{array}{*{20}{c}} 1 \\ 1 \\ t \end{array}} \right)$ , b = $\left( {\begin{array}{*{20}{c}} 0 \\ { - t} \\ {4t} \end{array}} \right)$ , where $t \in \mathbb{R}$ .

Find and simplify an expression for a • b in terms of $t$ .

[2]

a.

Hence or otherwise, find the values of $t$ for which the angle between a and b is obtuse .

[4]

b.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

a • b = $\left( {1 \times 0} \right) + \left( {1 \times - t} \right) + \left( {t \times 4t} \right)$ (M1)

= $- t + 4{t^2}$ A1

[2 marks]

a.

recognition that a • b = |a||b|cos θ (M1)

a • b < 0 or $- t + 4{t^2}$ < 0 or cos θ < 0 R1

Note: Allow ≤ for R1.

attempt to solve using sketch or sign diagram (M1)

$0 < t < \frac{1}{4}$ A1

[4 marks]

b.

Examiners report

[N/A]

a.

[N/A]

b.

Syllabus sections

Topic 3—Geometry and trigonometry » AHL 3.13—Scalar and vector products

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