Perplex
  • Lessons
  • Problems
  • Speed Run
  • Practice Tests
  • Skill Checklist
  • Review Videos
  • All Content
  • Landing Page
  • Sign Up
  • Login
  • Perplex
    IB Math AAHL
    /
    Vectors
    /

    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.

    Intersecting lines

    AHL 3.15

    Two vector lines intersect if they share exactly one common point. That means they are not parallel.


    For example, consider:

    r1​=⎝⎛​123​⎠⎞​+λ⎝⎛​400​⎠⎞​,r2​=⎝⎛​211​⎠⎞​+μ⎝⎛​312​⎠⎞​.

    Setting them equal, ⎝⎛​1+4λ23​⎠⎞​=⎝⎛​2+3μ1+μ1+2μ​⎠⎞​, leads to the system

    ⎩⎪⎨⎪⎧​1+4λ=2+3μ2=1+μ3=1+2μ​

    1+4λ=2+3μ, 2=1+μ, 3=1+2μ. Solving gives μ=1 and λ=1. Substituting back shows the unique intersection point is ⎝⎛​523​⎠⎞​.


    Powered by Desmos

    Intersecting lines

    AHL 3.15

    Two vector lines intersect if they share exactly one common point. That means they are not parallel.


    For example, consider:

    r1​=⎝⎛​123​⎠⎞​+λ⎝⎛​400​⎠⎞​,r2​=⎝⎛​211​⎠⎞​+μ⎝⎛​312​⎠⎞​.

    Setting them equal, ⎝⎛​1+4λ23​⎠⎞​=⎝⎛​2+3μ1+μ1+2μ​⎠⎞​, leads to the system

    ⎩⎪⎨⎪⎧​1+4λ=2+3μ2=1+μ3=1+2μ​

    1+4λ=2+3μ, 2=1+μ, 3=1+2μ. Solving gives μ=1 and λ=1. Substituting back shows the unique intersection point is ⎝⎛​523​⎠⎞​.


    Powered by Desmos

    Basics & Scalar ProductVector ProductLinesPlanes