Given that \(\overrightarrow{AB} = 5i + 3j\) and \(\overrightarrow{AC} = 2i + 5j\), find \(\overrightarrow{BC}\).
Question 1 Report
Given that \(\overrightarrow{AB} = 5i + 3j\) and \(\overrightarrow{AC} = 2i + 5j\), find \(\overrightarrow{BC}\).
Answer Details
To find \(\overrightarrow{BC}\), we need to subtract \(\overrightarrow{AB}\) from \(\overrightarrow{AC}\), as both of these vectors share the point \(A\).
So, \[\overrightarrow{BC} = \overrightarrow{AC} - \overrightarrow{AB}\]
Substituting the given values, we get:
\begin{align*}
\overrightarrow{BC} &= \overrightarrow{AC} - \overrightarrow{AB} \\
&= (2i + 5j) - (5i + 3j) \\
&= 2i + 5j - 5i - 3j \\
&= \boxed{-3i + 2j}
\end{align*}
Therefore, the answer is option (B) -3i + 2j.
Download The App On Google Playstore
Everything you need to excel in your exams
Personalized AI Learning Chat Assistant
200,000+ Exam Questions Across IGCSE, JAMB, WAEC & NECO
Over 3,900 Lesson Notes
Offline Support - Learn Anytime, Anywhere
Green Bridge Timetable
Literature Summaries & Potential Questions
Track Your Performance & Progress
In-depth Explanations for Comprehensive Learning