Two-dimensional vector arithmetic and magnitude · Short practice
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Recall
Two-dimensional vector arithmetic and magnitude — objective 1
Maths4U Original · Short practice
Vectors \(\displaystyle u=\)\(\left[\begin{matrix}3\\4\end{matrix}\right]\), \(\displaystyle v=\)\(\left[\begin{matrix}7\\2\end{matrix}\right]\) and \(\displaystyle w=2u-4v\).
Find the horizontal component of w.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Fresh review variant
Two-dimensional vector arithmetic and magnitude — objective 1
Maths4U Original · Short practice
Vectors \(\displaystyle u=\)\(\left[\begin{matrix}6\\8\end{matrix}\right]\), \(\displaystyle v=\)\(\left[\begin{matrix}8\\-2\end{matrix}\right]\) and \(\displaystyle w=2u-5v\).
Find the horizontal component of w.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Method
Two-dimensional vector arithmetic and magnitude — objective 2
Maths4U Original · Short practice
Vectors \(\displaystyle u=\)\(\left[\begin{matrix}6\\8\end{matrix}\right]\), \(\displaystyle v=\)\(\left[\begin{matrix}8\\-2\end{matrix}\right]\) and \(\displaystyle w=2u-5v\).
Find the vertical component of w.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Fresh review variant
Two-dimensional vector arithmetic and magnitude — objective 2
Maths4U Original · Short practice
Vectors \(\displaystyle u=\)\(\left[\begin{matrix}12\\16\end{matrix}\right]\), \(\displaystyle v=\)\(\left[\begin{matrix}3\\0\end{matrix}\right]\) and \(\displaystyle w=2u-3v\).
Find the vertical component of w.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Apply
Two-dimensional vector arithmetic and magnitude — objective 3
Maths4U Original · Short practice
Vectors \(\displaystyle u=\)\(\left[\begin{matrix}9\\12\end{matrix}\right]\), \(\displaystyle v=\)\(\left[\begin{matrix}2\\-1\end{matrix}\right]\) and \(\displaystyle w=2u-2v\).
Find the magnitude of u.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Fresh review variant
Two-dimensional vector arithmetic and magnitude — objective 3
Maths4U Original · Short practice
Vectors \(\displaystyle u=\)\(\left[\begin{matrix}12\\16\end{matrix}\right]\), \(\displaystyle v=\)\(\left[\begin{matrix}3\\0\end{matrix}\right]\) and \(\displaystyle w=2u-3v\).
Find the magnitude of u.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Check understanding
Two-dimensional vector arithmetic and magnitude — objective 4
Maths4U Original · Short practice
Vectors \(\displaystyle u=\)\(\left[\begin{matrix}12\\16\end{matrix}\right]\), \(\displaystyle v=\)\(\left[\begin{matrix}3\\0\end{matrix}\right]\) and \(\displaystyle w=2u-3v\).
Find the magnitude of 3u.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Fresh review variant
Two-dimensional vector arithmetic and magnitude — objective 4
Maths4U Original · Short practice
Vectors \(\displaystyle u=\)\(\left[\begin{matrix}15\\20\end{matrix}\right]\), \(\displaystyle v=\)\(\left[\begin{matrix}4\\1\end{matrix}\right]\) and \(\displaystyle w=2u-4v\).
Find the magnitude of 4u.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.