Three-dimensional position and displacement vectors · Short practice

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Recall

Position and displacement vectors in three dimensions — objective 1

Maths4U Original · Short practice

A has position vector \(\left[\begin{matrix}17\\2\\1\end{matrix}\right]\) and B has position vector \(\left[\begin{matrix}19\\4\\5\end{matrix}\right]\).

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.

Fresh review variant

Position and displacement vectors in three dimensions — objective 1

Maths4U Original · Short practice

A has position vector \(\left[\begin{matrix}18\\2\\2\end{matrix}\right]\) and B has position vector \(\left[\begin{matrix}21\\5\\7\end{matrix}\right]\).

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.

Method

Position and displacement vectors in three dimensions — objective 2

Maths4U Original · Short practice

A has position vector \(\left[\begin{matrix}18\\2\\2\end{matrix}\right]\) and B has position vector \(\left[\begin{matrix}21\\5\\7\end{matrix}\right]\).

Find the z-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.

Fresh review variant

Position and displacement vectors in three dimensions — objective 2

Maths4U Original · Short practice

A has position vector \(\left[\begin{matrix}19\\2\\3\end{matrix}\right]\) and B has position vector \(\left[\begin{matrix}20\\6\\9\end{matrix}\right]\).

Find the z-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.

Apply

Position and displacement vectors in three dimensions — objective 3

Maths4U Original · Short practice

A has position vector \(\left[\begin{matrix}19\\2\\3\end{matrix}\right]\) and B has position vector \(\left[\begin{matrix}20\\6\\9\end{matrix}\right]\).

Find \(\displaystyle |AB|^{2}\).

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.

Fresh review variant

Position and displacement vectors in three dimensions — objective 3

Maths4U Original · Short practice

A has position vector \(\left[\begin{matrix}20\\2\\4\end{matrix}\right]\) and B has position vector \(\left[\begin{matrix}22\\7\\11\end{matrix}\right]\).

Find \(\displaystyle |AB|^{2}\).

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.

Check understanding

Position and displacement vectors in three dimensions — objective 4

Maths4U Original · Short practice

A has position vector \(\left[\begin{matrix}20\\2\\4\end{matrix}\right]\) and B has position vector \(\left[\begin{matrix}22\\7\\11\end{matrix}\right]\).

Find the midpoint 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.

Fresh review variant

Position and displacement vectors in three dimensions — objective 4

Maths4U Original · Short practice

A has position vector \(\left[\begin{matrix}21\\2\\1\end{matrix}\right]\) and B has position vector \(\left[\begin{matrix}24\\4\\4\end{matrix}\right]\).

Find the midpoint 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.

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