Connected vector skills: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
A has position vector \(\left[\begin{matrix}22\\2\\2\end{matrix}\right]\) and B has position vector \(\left[\begin{matrix}23\\5\\6\end{matrix}\right]\).
Find the x-component of AB.
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.
Connected vector skills: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
A has position vector \(\left[\begin{matrix}23\\2\\3\end{matrix}\right]\) and B has position vector \(\left[\begin{matrix}25\\6\\8\end{matrix}\right]\).
Find the x-component of AB.
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.
Connected vector skills: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\mathbf u=\left[\begin{matrix}3\\2\\3\end{matrix}\right],\quad\mathbf v=\left[\begin{matrix}2\\2\\1\end{matrix}\right]\). Let θ be the angle between these two vectors in [0,π].
Find \(\displaystyle |u|^{2}\).
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.
Connected vector skills: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\mathbf u=\left[\begin{matrix}4\\2\\3\end{matrix}\right],\quad\mathbf v=\left[\begin{matrix}2\\3\\1\end{matrix}\right]\). Let θ be the angle between these two vectors in [0,π].
Find \(\displaystyle |u|^{2}\).
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.
Connected vector skills: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}24\\2\\3\end{matrix}\right]+t\left[\begin{matrix}3\\5\\6\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}21\\36\\18\end{matrix}\right]+u\left[\begin{matrix}6\\-3\\5\end{matrix}\right]\).
Find the intersection 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.
Connected vector skills: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}25\\2\\1\end{matrix}\right]+t\left[\begin{matrix}1\\2\\7\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}20\\7\\13\end{matrix}\right]+u\left[\begin{matrix}7\\-1\\2\end{matrix}\right]\).
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.
Connected vector skills: check 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.
Connected vector skills: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
The lines are \(\mathbf r=\left[\begin{matrix}26\\2\\3\end{matrix}\right]+t\left[\begin{matrix}1\\2\\2\end{matrix}\right]\), \(\mathbf r=\left[\begin{matrix}25\\10\\4\end{matrix}\right]+u\left[\begin{matrix}2\\-1\\3\end{matrix}\right]\).
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.