Watch comprehensive video reviews for most units, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
Vectors
Watch comprehensive video reviews for Vectors, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
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AHL 3.18
When three planes are considered together, their intersection in 3D space can take several forms:
A plane if all three planes coincide.
A single point if the three planes intersect uniquely, meaning their normal vectors are not all parallel or in some degenerate arrangement, and the system of equations has exactly one solution.
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A line if two planes intersect in a line and the third plane also contains that line (or if each pair of planes meets along the same line).
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No intersection if the system of equations is inconsistent (e.g., the planes are arranged in parallel or partially parallel ways that do not share a common point).
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AHL 3.18
When three planes are considered together, their intersection in 3D space can take several forms:
A plane if all three planes coincide.
A single point if the three planes intersect uniquely, meaning their normal vectors are not all parallel or in some degenerate arrangement, and the system of equations has exactly one solution.
Powered by Desmos
A line if two planes intersect in a line and the third plane also contains that line (or if each pair of planes meets along the same line).
Powered by Desmos
No intersection if the system of equations is inconsistent (e.g., the planes are arranged in parallel or partially parallel ways that do not share a common point).
Powered by Desmos