Vectors

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Question 21

Relative to a fixed origin $O$ , the vertex $D\,$ of a triangular structure has position vector $(4i−j+5k)(4\mathbf{i} - \mathbf{j} + 5\mathbf{k})$ , vertex $E\,$ has position vector $(5i+2j+9k)(5\mathbf{i} + 2\mathbf{j} + 9\mathbf{k})$ , and vertex $F\,$ has position vector $(i+3j+4k)(\mathbf{i} + 3\mathbf{j} + 4\mathbf{k})$ .

a.

Find the vector $EF⃗\vec{EF}$ .

[2]

b.

Show that the quadrilateral $ODEF\,$ is a parallelogram, giving reasons for your answer.

[3]

Vectors

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Question 21

Relative to a fixed origin $O$ , the vertex $D\,$ of a triangular structure has position vector $(4i−j+5k)(4\mathbf{i} - \mathbf{j} + 5\mathbf{k})$ , vertex $E\,$ has position vector $(5i+2j+9k)(5\mathbf{i} + 2\mathbf{j} + 9\mathbf{k})$ , and vertex $F\,$ has position vector $(i+3j+4k)(\mathbf{i} + 3\mathbf{j} + 4\mathbf{k})$ .

a.

Find the vector $EF⃗\vec{EF}$ .

[2]

b.

Show that the quadrilateral $ODEF\,$ is a parallelogram, giving reasons for your answer.

[3]

Vectors

Question 21

Vectors Questions

Vectors

Question 21

Vectors Questions