Intersecting and skew lines: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}21\\2\\3\end{matrix}\right]+t\left[\begin{matrix}1\\2\\3\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}17\\9\\3\end{matrix}\right]+u\left[\begin{matrix}2\\-1\\2\end{matrix}\right]\).
Which statement describes the two lines?
Choose one answer.
Intersecting and skew lines: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}22\\2\\3\end{matrix}\right]+t\left[\begin{matrix}1\\2\\1\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}23\\9\\5\end{matrix}\right]+u\left[\begin{matrix}2\\-1\\3\end{matrix}\right]\).
Which statement describes the two lines?
Choose one answer.
Intersecting and skew lines: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}22\\2\\3\end{matrix}\right]+t\left[\begin{matrix}1\\2\\1\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}23\\9\\5\end{matrix}\right]+u\left[\begin{matrix}2\\-1\\3\end{matrix}\right]\).
Find t when the x and y coordinates match.
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.
Intersecting and skew lines: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}23\\2\\3\end{matrix}\right]+t\left[\begin{matrix}1\\2\\2\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}23\\12\\3\end{matrix}\right]+u\left[\begin{matrix}2\\-1\\4\end{matrix}\right]\).
Find t when the x and y coordinates match.
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.
Intersecting and skew lines: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}23\\2\\3\end{matrix}\right]+t\left[\begin{matrix}1\\2\\2\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}23\\12\\3\end{matrix}\right]+u\left[\begin{matrix}2\\-1\\4\end{matrix}\right]\).
Find u when the x and y coordinates of the two lines match.
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.
Intersecting and skew lines: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}24\\2\\3\end{matrix}\right]+t\left[\begin{matrix}1\\2\\3\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}23\\15\\7\end{matrix}\right]+u\left[\begin{matrix}2\\-1\\5\end{matrix}\right]\).
Find u when the x and y coordinates of the two lines match.
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.
Intersecting and skew lines: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}24\\2\\3\end{matrix}\right]+t\left[\begin{matrix}1\\2\\3\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}23\\15\\7\end{matrix}\right]+u\left[\begin{matrix}2\\-1\\5\end{matrix}\right]\).
At the parameters making the x and y coordinates match, find second-line z minus first-line z.
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.
Intersecting and skew lines: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}25\\2\\3\end{matrix}\right]+t\left[\begin{matrix}1\\2\\1\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}25\\7\\3\end{matrix}\right]+u\left[\begin{matrix}2\\-1\\2\end{matrix}\right]\).
At the parameters making the x and y coordinates match, find second-line z minus first-line z.
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.