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Date	May 2019	Marks available	4	Reference code	19M.1.SL.TZ2.S_2
Level	Standard Level	Paper	Paper 1	Time zone	Time zone 2
Command term	Find	Question number	S_2	Adapted from	N/A

Question

Consider the vectors a = $⎛ ⎜ ⎝ \begin{matrix} 03 p \end{matrix} ⎞ ⎟ ⎠$ $\left( {\begin{array}{*{20}{c}} 0 \\ 3 \\ p \end{array}} \right)$ and b = $⎛ ⎜ ⎝ \begin{matrix} 0618 \end{matrix} ⎞ ⎟ ⎠$ $\left( {\begin{array}{*{20}{c}} 0 \\ 6 \\ {18} \end{array}} \right)$ .

Find the value of $p$ $p$ for which a and b are

parallel.

[2]

a.

perpendicular.

[4]

b.

Markscheme

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

valid approach (M1)

eg b = 2a, a = $k$ $k$ b, cos θ = 1, a•b = −|a||b|, 2 $p$ $p$ = 18

$p$ $p$ = 9 A1 N2

[2 marks]

a.

evidence of scalar product (M1)

eg a•b, (0)(0) + (3)(6) + $p$ $p$ (18)

recognizing a•b = 0 (seen anywhere) (M1)

correct working (A1)

eg 18 + 18 $p$ $p$ = 0, 18 $p$ $p$ = −18 (A1)

$p$ $p$ = −1 A1 N3

[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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