Vectors

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

Question 25

The points $A\,$ and $B\,$ have position vectors $(1−24)\begin{pmatrix} 1 \\ -2 \\ 4 \end{pmatrix}$ and $(3−52)\begin{pmatrix} 3 \\ -5 \\ 2 \end{pmatrix}$ respectively.

a.

Find the exact length of $A B$ .

[2]

b.

Find the position vector of the midpoint of $A B$ .

[2]

c.

The points $P\,$ and $Q\,$ have position vectors $(421)\begin{pmatrix} 4 \\ 2 \\ 1 \end{pmatrix}$ and $(253)\begin{pmatrix} 2 \\ 5 \\ 3 \end{pmatrix}$ respectively. Show that $ABPQ\,$ is a parallelogram.

[3]

Vectors

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

Question 25

The points $A\,$ and $B\,$ have position vectors $(1−24)\begin{pmatrix} 1 \\ -2 \\ 4 \end{pmatrix}$ and $(3−52)\begin{pmatrix} 3 \\ -5 \\ 2 \end{pmatrix}$ respectively.

a.

Find the exact length of $A B$ .

[2]

b.

Find the position vector of the midpoint of $A B$ .

[2]

c.

The points $P\,$ and $Q\,$ have position vectors $(421)\begin{pmatrix} 4 \\ 2 \\ 1 \end{pmatrix}$ and $(253)\begin{pmatrix} 2 \\ 5 \\ 3 \end{pmatrix}$ respectively. Show that $ABPQ\,$ is a parallelogram.

[3]

Vectors

Question 25

Vectors Questions

Vectors

Question 25

Vectors Questions