LEARN · EXPLAIN · REVISE

Find the distance from P to the plane.

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

P=(27,0,0),\quad \Pi:3x+4y=0

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.

d=|3x_P+4y_P|/5

Worked solution

Use the dot product to connect coordinates with length or angle.
Apply the stated relation and retain its conditions.
$d=3(27)/\sqrt{3^2+4^2}=16.2$
Normalize the plane normal; raw substitution is not a distance.

The requested value is 16.2.

Checks and common pitfalls: Normalize the plane normal; raw substitution is not a distance.

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

Teacher preparation and assessment