AI generatedGeometry and measuresGCSE Higher / IGCSE Extended

Comparing coefficients of independent vectors

Comparing coefficients of independent vectors.

  • Write two routes to the same point and collect the a- and -components.
  • If a and are non-parallel, their coefficients must match separately.
  • Solve the resulting equations with a labelled operation at each step. A parameter is a fraction of its whole directed segment.

Example 1

a and are non-parallel. Write the two scalar equations obtained by comparing vector coefficients. Do not solve them yet.

a-componentsThe coefficient of a must match on both sides.
b-componentsThe coefficient of must also match.
These two equations can now be solved simultaneously.

Example 2

a and are non-parallel. Write the two scalar equations obtained by comparing vector coefficients. Do not solve them yet.

a-componentsThe coefficient of a must match on both sides.
b-componentsThe coefficient of must also match.
These two equations can now be solved simultaneously.

Your turn

Question 1

a and are non-parallel. Write the two scalar equations obtained by comparing vector coefficients. Do not solve them yet.

Check answer
a-componentsThe coefficient of a must match on both sides.
b-componentsThe coefficient of must also match.
These two equations can now be solved simultaneously.
Question 2

a and are non-parallel. Write the two scalar equations obtained by comparing vector coefficients. Do not solve them yet.

Check answer
a-componentsThe coefficient of a must match on both sides.
b-componentsThe coefficient of must also match.
These two equations can now be solved simultaneously.
Question 3

a and are non-parallel. Write the two scalar equations obtained by comparing vector coefficients. Do not solve them yet.

Check answer
a-componentsThe coefficient of a must match on both sides.
b-componentsThe coefficient of must also match.
These two equations can now be solved simultaneously.
Question 4

a and are non-parallel. Write the two scalar equations obtained by comparing vector coefficients. Do not solve them yet.

Check answer
a-componentsThe coefficient of a must match on both sides.
b-componentsThe coefficient of must also match.
These two equations can now be solved simultaneously.
Question 5

a and are non-parallel. Write the two scalar equations obtained by comparing vector coefficients. Do not solve them yet.

Check answer
a-componentsThe coefficient of a must match on both sides.
b-componentsThe coefficient of must also match.
These two equations can now be solved simultaneously.
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