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 6

The points $A\,$ and $B\,$ have position vectors $−3)\begin{pmatrix} 2 \ 1 \ -3 \end{pmatrix}$ and $0)\begin{pmatrix} 5 \ -1 \ 0 \end{pmatrix}$ respectively.

a.

Find the exact length of $A B$ .

[2]

b.

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

[1]

c.

The points $P\,$ and $Q\,$ have position vectors $1)\begin{pmatrix} 4 \ 2 \ 1 \end{pmatrix}$ and $−2)\begin{pmatrix} 1 \ 4 \ -2 \end{pmatrix}$ 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 6

The points $A\,$ and $B\,$ have position vectors $−3)\begin{pmatrix} 2 \ 1 \ -3 \end{pmatrix}$ and $0)\begin{pmatrix} 5 \ -1 \ 0 \end{pmatrix}$ respectively.

a.

Find the exact length of $A B$ .

[2]

b.

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

[1]

c.

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

[3]

Vectors

Question 6

Vectors Questions

Vectors

Question 6

Vectors Questions