Vectors

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Question 13

The points $A\,$ and $B\,$ have position vectors $1)\begin{pmatrix} 3 \ -2 \ 1 \end{pmatrix}$ and $−1)\begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}$ 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 $3)\begin{pmatrix} 2 \ 1 \ 3 \end{pmatrix}$ and $5)\begin{pmatrix} 4 \ -3 \ 5 \end{pmatrix}$ respectively. Show that $ABPQ\,$ is a parallelogram.

[3]

Vectors

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Question 13

The points $A\,$ and $B\,$ have position vectors $1)\begin{pmatrix} 3 \ -2 \ 1 \end{pmatrix}$ and $−1)\begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}$ 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 $3)\begin{pmatrix} 2 \ 1 \ 3 \end{pmatrix}$ and $5)\begin{pmatrix} 4 \ -3 \ 5 \end{pmatrix}$ respectively. Show that $ABPQ\,$ is a parallelogram.

[3]

Vectors

Question 13

Vectors Questions

Vectors

Question 13

Vectors Questions