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    IB Math AAHL
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    Vectors
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    Video

    Video Reviews

    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

    Video Reviews

    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.

    Basics & Scalar ProductVector ProductLinesPlanes

    The video will automatically pause when it reaches a problem.

    Angle between 2 planes

    AHL 3.18

    The angle θ between two planes can be found by computing the angle between the two plane normals.


    problem image


    Example

    Find the angle between the planes

    2x+y−z2x−y+z​=6=2​


    The normals are n1​=⎝⎛​21−1​⎠⎞​ and n2​=⎝⎛​2−11​⎠⎞​, both with magnitude √6. So

    cosθ=√6⋅√62⋅2+1⋅(−1)+(−1)⋅1​=31​

    So

    θ=cos−1(31​)=70.5°

    Angle between 2 planes

    AHL 3.18

    The angle θ between two planes can be found by computing the angle between the two plane normals.


    problem image


    Example

    Find the angle between the planes

    2x+y−z2x−y+z​=6=2​


    The normals are n1​=⎝⎛​21−1​⎠⎞​ and n2​=⎝⎛​2−11​⎠⎞​, both with magnitude √6. So

    cosθ=√6⋅√62⋅2+1⋅(−1)+(−1)⋅1​=31​

    So

    θ=cos−1(31​)=70.5°
    Basics & Scalar ProductVector ProductLinesPlanes