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Recall
Vector ratios and geometric proofs — objective 1
Maths4U Original · Short practice
\(\displaystyle OA=\)\(\left[\begin{matrix}16\\2\end{matrix}\right]\), \(\displaystyle OB=\)\(\left[\begin{matrix}1\\18\end{matrix}\right]\). M divides AB with \(\displaystyle AM:MB=1:5\). For the general ratio formula write \(\displaystyle m=1, n=5\).
Write \(\mathbf a=\overrightarrow{OA}\) and \(\mathbf b=\overrightarrow{OB}\).
Find the x-coordinate of M.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Fresh review variant
Vector ratios and geometric proofs — objective 1
Maths4U Original · Short practice
\(\displaystyle OA=\)\(\left[\begin{matrix}17\\2\end{matrix}\right]\), \(\displaystyle OB=\)\(\left[\begin{matrix}1\\19\end{matrix}\right]\). M divides AB with \(\displaystyle AM:MB=2:2\). For the general ratio formula write \(\displaystyle m=2, n=2\).
Write \(\mathbf a=\overrightarrow{OA}\) and \(\mathbf b=\overrightarrow{OB}\).
Find the x-coordinate of M.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Method
Vector ratios and geometric proofs — objective 2
Maths4U Original · Short practice
\(\displaystyle OA=\)\(\left[\begin{matrix}17\\2\end{matrix}\right]\), \(\displaystyle OB=\)\(\left[\begin{matrix}1\\19\end{matrix}\right]\). M divides AB with \(\displaystyle AM:MB=2:2\). For the general ratio formula write \(\displaystyle m=2, n=2\).
Write \(\mathbf a=\overrightarrow{OA}\) and \(\mathbf b=\overrightarrow{OB}\).
Find the y-coordinate of M.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Fresh review variant
Vector ratios and geometric proofs — objective 2
Maths4U Original · Short practice
\(\displaystyle OA=\)\(\left[\begin{matrix}18\\2\end{matrix}\right]\), \(\displaystyle OB=\)\(\left[\begin{matrix}1\\20\end{matrix}\right]\). M divides AB with \(\displaystyle AM:MB=3:3\). For the general ratio formula write \(\displaystyle m=3, n=3\).
Write \(\mathbf a=\overrightarrow{OA}\) and \(\mathbf b=\overrightarrow{OB}\).
Find the y-coordinate of M.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Apply
Vector ratios and geometric proofs — objective 3
Maths4U Original · Short practice
\(\displaystyle OA=\)\(\left[\begin{matrix}18\\2\end{matrix}\right]\), \(\displaystyle OB=\)\(\left[\begin{matrix}1\\20\end{matrix}\right]\). M divides AB with \(\displaystyle AM:MB=3:3\). For the general ratio formula write \(\displaystyle m=3, n=3\).
Write \(\mathbf a=\overrightarrow{OA}\) and \(\mathbf b=\overrightarrow{OB}\).
Find the coefficient of a in OM.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Fresh review variant
Vector ratios and geometric proofs — objective 3
Maths4U Original · Short practice
\(\displaystyle OA=\)\(\left[\begin{matrix}19\\2\end{matrix}\right]\), \(\displaystyle OB=\)\(\left[\begin{matrix}1\\21\end{matrix}\right]\). M divides AB with \(\displaystyle AM:MB=1:4\). For the general ratio formula write \(\displaystyle m=1, n=4\).
Write \(\mathbf a=\overrightarrow{OA}\) and \(\mathbf b=\overrightarrow{OB}\).
Find the coefficient of a in OM.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Check understanding
Vector ratios and geometric proofs — objective 4
Maths4U Original · Short practice
\(\displaystyle OA=\)\(\left[\begin{matrix}19\\2\end{matrix}\right]\), \(\displaystyle OB=\)\(\left[\begin{matrix}1\\21\end{matrix}\right]\). M divides AB with \(\displaystyle AM:MB=1:4\). For the general ratio formula write \(\displaystyle m=1, n=4\).
Write \(\mathbf a=\overrightarrow{OA}\) and \(\mathbf b=\overrightarrow{OB}\).
Find the coefficient of b in OM.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Fresh review variant
Vector ratios and geometric proofs — objective 4
Maths4U Original · Short practice
\(\displaystyle OA=\)\(\left[\begin{matrix}20\\2\end{matrix}\right]\), \(\displaystyle OB=\)\(\left[\begin{matrix}1\\22\end{matrix}\right]\). M divides AB with \(\displaystyle AM:MB=2:5\). For the general ratio formula write \(\displaystyle m=2, n=5\).
Write \(\mathbf a=\overrightarrow{OA}\) and \(\mathbf b=\overrightarrow{OB}\).
Find the coefficient of b in OM.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.