End-of-chapter review exercise 6: check 1
Difficulty: ★★☆Maths4U Original · Short practice
\(a=\left[\begin{matrix}12\\1\\0\end{matrix}\right],\ b=\left[\begin{matrix}0\\1\\13\end{matrix}\right]\). Let c=a×b.
Find the first component of c.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
End-of-chapter review exercise 6: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
\(a=\left[\begin{matrix}13\\1\\0\end{matrix}\right],\ b=\left[\begin{matrix}0\\1\\14\end{matrix}\right]\). Let c=a×b.
Find the first component of c.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
End-of-chapter review exercise 6: check 2
Difficulty: ★★☆Maths4U Original · Short practice
\(a=\left[\begin{matrix}13\\1\\0\end{matrix}\right],\ b=\left[\begin{matrix}0\\1\\14\end{matrix}\right]\). Let c=a×b.
Find the second component of c.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
End-of-chapter review exercise 6: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
\(a=\left[\begin{matrix}14\\1\\0\end{matrix}\right],\ b=\left[\begin{matrix}0\\1\\15\end{matrix}\right]\). Let c=a×b.
Find the second component of c.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
End-of-chapter review exercise 6: check 3
Difficulty: ★★☆Maths4U Original · Short practice
The line \(r=\left[\begin{matrix}15\\27\\3\end{matrix}\right]+t\left[\begin{matrix}1\\1\\1\end{matrix}\right]\) meets the plane \(x+2y+2z=16\).
Find the distance from P to the plane.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
End-of-chapter review exercise 6: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
The line \(r=\left[\begin{matrix}16\\29\\3\end{matrix}\right]+t\left[\begin{matrix}1\\1\\1\end{matrix}\right]\) meets the plane \(x+2y+2z=17\).
Find the distance from P to the plane.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
End-of-chapter review exercise 6: check 4
Difficulty: ★★☆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.
End-of-chapter review exercise 6: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
Two lines have \(r=t\left[\begin{matrix}1\\16\\0\end{matrix}\right]\) and \(r=\left[\begin{matrix}18\\0\\1\end{matrix}\right]+u\left[\begin{matrix}0\\1\\17\end{matrix}\right]\). 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.