Planes: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
The line \(r=\left[\begin{matrix}12\\21\\3\end{matrix}\right]+t\left[\begin{matrix}1\\1\\1\end{matrix}\right]\) meets the plane \(x+2y+2z=13\).
Find the intersection parameter t.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Planes: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
The line \(r=\left[\begin{matrix}13\\23\\3\end{matrix}\right]+t\left[\begin{matrix}1\\1\\1\end{matrix}\right]\) meets the plane \(x+2y+2z=14\).
Find the intersection parameter t.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Planes: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
The line \(r=\left[\begin{matrix}13\\23\\3\end{matrix}\right]+t\left[\begin{matrix}1\\1\\1\end{matrix}\right]\) meets the plane \(x+2y+2z=14\).
Find the intersection x-coordinate.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Planes: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
The line \(r=\left[\begin{matrix}14\\25\\3\end{matrix}\right]+t\left[\begin{matrix}1\\1\\1\end{matrix}\right]\) meets the plane \(x+2y+2z=15\).
Find the intersection x-coordinate.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Planes: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Two lines have \(r=t\left[\begin{matrix}1\\13\\0\end{matrix}\right]\) and \(r=\left[\begin{matrix}15\\0\\1\end{matrix}\right]+u\left[\begin{matrix}0\\1\\14\end{matrix}\right]\). For the line-plane question, b is the normal to a separate plane.
Find the shortest distance between the two lines.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Planes: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Two lines have \(r=t\left[\begin{matrix}1\\14\\0\end{matrix}\right]\) and \(r=\left[\begin{matrix}16\\0\\1\end{matrix}\right]+u\left[\begin{matrix}0\\1\\15\end{matrix}\right]\). For the line-plane question, b is the normal to a separate plane.
Find the shortest distance between the two lines.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Planes: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Two lines have \(r=t\left[\begin{matrix}1\\14\\0\end{matrix}\right]\) and \(r=\left[\begin{matrix}16\\0\\1\end{matrix}\right]+u\left[\begin{matrix}0\\1\\15\end{matrix}\right]\). For the line-plane question, b is the normal to a separate plane.
Find the acute angle in degrees between direction a and a plane with normal b.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Planes: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Two lines have \(r=t\left[\begin{matrix}1\\15\\0\end{matrix}\right]\) and \(r=\left[\begin{matrix}17\\0\\1\end{matrix}\right]+u\left[\begin{matrix}0\\1\\16\end{matrix}\right]\). For the line-plane question, b is the normal to a separate plane.
Find the acute angle in degrees between direction a and a plane with normal b.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.