LEARN · EXPLAIN · REVISE

Find cos θ between a and b.

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 / Standard#Your turn

a=(1,1,0), b=(0,26,1)

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.

cosθ=(a·b)/(|a||b|)

Worked solution

Use the dot product to connect coordinates with length or angle.
Apply the stated relation and retain its conditions.
$a\cdot b=26, |a|=\sqrt2, |b|=\sqrt{677}$
Apply the stated relation and retain its conditions.
$\cos\theta=26/\sqrt{1354}$
Both vector lengths enter the denominator.

The requested value is 0.706584352758.

Checks and common pitfalls: Both vector lengths enter the denominator.

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

Teacher preparation and assessment