Vector equations of lines and intersections · Short practice
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Recall
Vector lines and intersections — objective 1
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}20\\2\\2\end{matrix}\right]+t\left[\begin{matrix}2\\5\\7\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}16\\31\\27\end{matrix}\right]+u\left[\begin{matrix}7\\-2\\5\end{matrix}\right]\).
Find the parameter t at the intersection.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
Vector lines and intersections — objective 1
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}21\\2\\3\end{matrix}\right]+t\left[\begin{matrix}3\\2\\3\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}18\\15\\3\end{matrix}\right]+u\left[\begin{matrix}3\\-3\\2\end{matrix}\right]\).
Find the parameter t at the intersection.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Method
Vector lines and intersections — objective 2
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}21\\2\\3\end{matrix}\right]+t\left[\begin{matrix}3\\2\\3\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}18\\15\\3\end{matrix}\right]+u\left[\begin{matrix}3\\-3\\2\end{matrix}\right]\).
Find the second parameter u.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
Vector lines and intersections — objective 2
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}22\\2\\1\end{matrix}\right]+t\left[\begin{matrix}1\\3\\4\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}21\\12\\10\end{matrix}\right]+u\left[\begin{matrix}4\\-1\\3\end{matrix}\right]\).
Find the second parameter u.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Apply
Vector lines and intersections — objective 3
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}22\\2\\1\end{matrix}\right]+t\left[\begin{matrix}1\\3\\4\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}21\\12\\10\end{matrix}\right]+u\left[\begin{matrix}4\\-1\\3\end{matrix}\right]\).
Find the intersection x-coordinate.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
Vector lines and intersections — objective 3
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}23\\2\\2\end{matrix}\right]+t\left[\begin{matrix}2\\4\\5\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}21\\22\\14\end{matrix}\right]+u\left[\begin{matrix}5\\-2\\4\end{matrix}\right]\).
Find the intersection x-coordinate.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Check understanding
Vector lines and intersections — objective 4
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}23\\2\\2\end{matrix}\right]+t\left[\begin{matrix}2\\4\\5\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}21\\22\\14\end{matrix}\right]+u\left[\begin{matrix}5\\-2\\4\end{matrix}\right]\).
Find the intersection y-coordinate.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
Vector lines and intersections — objective 4
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}24\\2\\3\end{matrix}\right]+t\left[\begin{matrix}3\\5\\6\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}21\\36\\18\end{matrix}\right]+u\left[\begin{matrix}6\\-3\\5\end{matrix}\right]\).
Find the intersection y-coordinate.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.