Easy -1.3 This is a straightforward two-step question: find the vector AB by subtraction, then calculate its magnitude using Pythagoras. It requires only basic vector operations and is a standard textbook exercise with no problem-solving element.
5 You are given that \(\overrightarrow { \mathrm { OA } } = \binom { 3 } { - 1 }\) and \(\overrightarrow { \mathrm { OB } } = \binom { 5 } { - 3 }\).
Determine the exact length of \(A B\).
may be in coordinate form or may see distances identified on diagram; may be implied by \(\sqrt{(\pm2)^2 + (\pm2)^2}\) oe
\(\sqrt{(\pm2)^2 + (\pm2)^2}\) oe
M1 (1.1)
or FT their evaluation of \(\binom{5}{-3} - \binom{3}{-1}\); may be implied by correct answer
\(\sqrt{8}\) or \(2\sqrt{2}\) isw
A1 (1.1)
if B0M0, allow SC1 for \(\sqrt{80}\) or \(4\sqrt{5}\) (from addition of vectors) if supported by Pythagoras; if B0M0 allow SC1 for \(\sqrt{8}\) or \(2\sqrt{2}\) unsupported
## Question 5:
$\binom{5}{-3} - \binom{3}{-1} = \binom{2}{-2}$ or $\binom{3}{-1} - \binom{5}{-3} = \binom{-2}{2}$ | B1 (2.1) | may be in coordinate form or may see distances identified on diagram; may be implied by $\sqrt{(\pm2)^2 + (\pm2)^2}$ oe
$\sqrt{(\pm2)^2 + (\pm2)^2}$ oe | M1 (1.1) | or FT their evaluation of $\binom{5}{-3} - \binom{3}{-1}$; may be implied by correct answer
$\sqrt{8}$ or $2\sqrt{2}$ isw | A1 (1.1) | if B0M0, allow SC1 for $\sqrt{80}$ or $4\sqrt{5}$ (from addition of vectors) if supported by Pythagoras; if B0M0 allow SC1 for $\sqrt{8}$ or $2\sqrt{2}$ unsupported
5 You are given that $\overrightarrow { \mathrm { OA } } = \binom { 3 } { - 1 }$ and $\overrightarrow { \mathrm { OB } } = \binom { 5 } { - 3 }$.
Determine the exact length of $A B$.
\hfill \mbox{\textit{OCR MEI Paper 2 2023 Q5 [3]}}