AI generatedGeometry and measuresGCSE Higher

Vectors dividing a line in a ratio

Use the correct fraction along the segment.

  • 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

M divides AB in the ratio AM:MB = 1:2.

Find the whole directed vector from A to B.Use 1 of the 3 total ratio parts.Add the route O → A → M.

Find the position vector of M. The denominator uses the total number of parts.

Example 2

M divides AB in the ratio AM:MB = 2:2.

Find the whole directed vector from A to B.Use 2 of the 4 total ratio parts.Add the route O → A → M.

Find the position vector of M. The denominator uses the total number of parts.

Your turn

Question 1

M divides AB in the ratio AM:MB = 3:2.

Check answer
Find the whole directed vector from A to B.Use 3 of the 5 total ratio parts.Add the route O → A → M.
Question 2

M divides AB in the ratio AM:MB = 4:2.

Check answer
Find the whole directed vector from A to B.Use 4 of the 6 total ratio parts.Add the route O → A → M.
Question 3

M divides AB in the ratio AM:MB = 5:2.

Check answer
Find the whole directed vector from A to B.Use 5 of the 7 total ratio parts.Add the route O → A → M.
Question 4

M divides AB in the ratio AM:MB = 1:3.

Check answer
Find the whole directed vector from A to B.Use 1 of the 4 total ratio parts.Add the route O → A → M.
Question 5

M divides AB in the ratio AM:MB = 2:3.

Check answer
Find the whole directed vector from A to B.Use 2 of the 5 total ratio parts.Add the route O → A → M.
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