LEARN · EXPLAIN · REVISE

Find λ so that a and b are perpendicular.

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 / Foundation#Your turn

a=(1,2,3),\ b=(22,1,\lambda)

Projection requires a nonzero direction; signed scalar projection can be negative.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use the dot product to connect coordinates with length or angle.

Hint 2

Use this intermediate relation.

a\cdot b=0

Worked solution

The requested value is -8.

Checks and common pitfalls: Use a zero dot product, not componentwise multiplication equal to zero.

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

Teacher preparation and assessment