19M.1.SL.TZ2.S_2

pestleMathematicsAASLPaper 119M· ahl-3-12-vector-definitionssource ↗

Consider the vectors a = $\left( {\begin{array}{*{20}{c}} 0 \\ 3 \\ p \end{array}} \right)$ and b = $\left( {\begin{array}{*{20}{c}} 0 \\ 6 \\ {18} \end{array}} \right)$ .

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

parallel.

[2]

perpendicular.

[4]

Markscheme / solution

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

$p$ = 9 A1 N2

[2 marks]

evidence of scalar product (M1)

eg a•b, (0)(0) + (3)(6) + $p$ (18)

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

correct working (A1)

eg 18 + 18 $p$ = 0, 18 $p$ = −18 (A1)

$p$ = −1 A1 N3

[4 marks]

Examiners’ report

[N/A]