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    IB Math AAHL
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    Vectors
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    Watch comprehensive video reviews for most units, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

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    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

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    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.

    Intersection of line and plane

    AHL 3.18

    To find the intersection of a line and a plane, substitute the vector line equation into the plane equation and solve for the parameter λ.


    For example, suppose we have the line:

    r=⎝⎛​121​⎠⎞​+λ⎝⎛​2−13​⎠⎞​

    and the plane:

    x+y−z=3

    Substituting the line into the plane gives:

    (1+2λ)+(2−λ)−(1+3λ)=3

    Expanding:

    2−2λ=3⇒λ=−21​

    Substituting this back into the line gives the intersection point:

    r=⎝⎛​121​⎠⎞​−21​⎝⎛​2−13​⎠⎞​=⎝⎛​02.5−0.5​⎠⎞​

    Intersection of line and plane

    AHL 3.18

    To find the intersection of a line and a plane, substitute the vector line equation into the plane equation and solve for the parameter λ.


    For example, suppose we have the line:

    r=⎝⎛​121​⎠⎞​+λ⎝⎛​2−13​⎠⎞​

    and the plane:

    x+y−z=3

    Substituting the line into the plane gives:

    (1+2λ)+(2−λ)−(1+3λ)=3

    Expanding:

    2−2λ=3⇒λ=−21​

    Substituting this back into the line gives the intersection point:

    r=⎝⎛​121​⎠⎞​−21​⎝⎛​2−13​⎠⎞​=⎝⎛​02.5−0.5​⎠⎞​
    Basics & Scalar ProductVector ProductLinesPlanes