Math Problem Statement

The image contains multiple math problems related to vector geometry and plane equations, such as finding vector equations of planes, angles between vectors, and line equations in 3D space.

Solution

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Math Problem Analysis

Mathematical Concepts

Vector Geometry
Plane Equations
3D Coordinate Geometry
Dot Product
Cross Product
Angles Between Vectors
Linear Equations

Formulas

Vector equation of a plane: r = r0 + λ1v1 + λ2v2
Dot product formula: A · B = |A| |B| cos(θ)
Cross product formula: A × B = |A| |B| sin(θ) n
Equation of a line: (x - x0) / a = (y - y0) / b = (z - z0) / c

Theorems

The Dot Product Theorem
The Cross Product Theorem
Equation of a plane and line in 3D

Suitable Grade Level

Grades 11-12

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