LEARN · EXPLAIN · REVISE

Explain why these three vectors do not give unique coefficients.

Read the idea, work independently, then explain what changed.

TOPIC 01

Space vectors and solid geometry: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Transfer#Your turn

e_1=(1,0,0), e_2=(0,1,0), e_3=(33,1,0)

A basis must be independent. Weights representing a point in a plane sum to one.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use vector components and the distributive laws.

Hint 2

Use this intermediate relation.

e_3=te_1+e_2

Worked solution

Use vector components and the distributive laws.
Apply the stated relation and retain its conditions.
$(33,1,0)=33(1,0,0)+(0,1,0)$
The dependent triple permits more than one representation.

The requested relation or conclusion is shown below.

e_3=33e_1+e_2

Checks and common pitfalls: The dependent triple permits more than one representation.

Reasoning checklist · self / teacher assessment

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment