AI generatedGeometry and measuresGCSE Higher / IGCSE Extended

Recognising scalar multiples in vector proofs

Recognising scalar multiples in vector proofs.

  • A vector has both magnitude and direction. Reverse a route by changing its sign.
  • Use a consistent direction and match corresponding components.
  • A scalar multiple proves parallel directions. Collinearity also needs a shared point.

Example 1

Show that and are parallel. State whether they point in the same or opposite directions.

Factor out the same scalar from both components.A scalar multiple has parallel direction.
Parallel; the same direction because the scalar is positive.

Example 2

Show that and are parallel. State whether they point in the same or opposite directions.

Factor out the same scalar from both components.A scalar multiple has parallel direction.
Parallel; opposite directions because the scalar is negative.

Your turn

Question 1

Show that and are parallel. State whether they point in the same or opposite directions.

Check answer
Factor out the same scalar from both components.A scalar multiple has parallel direction.
Parallel; the same direction because the scalar is positive.
Question 2

Show that and are parallel. State whether they point in the same or opposite directions.

Check answer
Factor out the same scalar from both components.A scalar multiple has parallel direction.
Parallel; opposite directions because the scalar is negative.
Question 3

Show that and are parallel. State whether they point in the same or opposite directions.

Check answer
Factor out the same scalar from both components.A scalar multiple has parallel direction.
Parallel; the same direction because the scalar is positive.
Question 4

Show that and are parallel. State whether they point in the same or opposite directions.

Check answer
Factor out the same scalar from both components.A scalar multiple has parallel direction.
Parallel; opposite directions because the scalar is negative.
Question 5

Show that and are parallel. State whether they point in the same or opposite directions.

Check answer
Factor out the same scalar from both components.A scalar multiple has parallel direction.
Parallel; the same direction because the scalar is positive.
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