Find the angle between two planes by calculating the acute angle between their normal vectors.

Vault Of Euclid

Angle Between Two Planes

Vector spaces warmup

Find the measure of the angle between planes \( x+y-z=3 \) and \( 3x-y+3z=5 \). Give the answer in radians and round to two decimal places.

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What you need first

Extracting normal vectors from plane equations
Calculating the dot product of two vectors
Calculating the magnitude of a vector
Using the inverse cosine function

What this problem tests

Tests the ability to extract normal vectors from plane equations and apply the dot product formula to find the angle between them.

This is a standard introductory problem in multivariable calculus or 3D analytic geometry, testing the geometric interpretation of plane equations and vector operations.

Angle Between Two Planes

What you need first

What this problem tests

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