LEARN · EXPLAIN · REVISE

A unit direction has cos²α=1/t², cos²β=1/9. Find cos²γ.

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

t=34

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.

cos²α+cos²β+cos²γ=1

Worked solution

Use the dot product to connect coordinates with length or angle.
Apply the stated relation and retain its conditions.
$\cos^2\gamma=1-1/1156-1/9$
The squared direction cosines sum to one.

The requested value is 0.888023836986.

Checks and common pitfalls: The squared direction cosines sum to one.

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

Teacher preparation and assessment