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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
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 3.14
The angle between two lines is simply the angle between their direction vectors.
Example
Find the acute angle between the lines 3x−5=2y+2=z+1 and ⎝⎛13−5⎠⎞+λ⎝⎛312⎠⎞.
The direction vector of 2x−5=2y+2=z+1 is ⎝⎛321⎠⎞.
Both direction vectors have magnitude
so
AHL 3.14
The angle between two lines is simply the angle between their direction vectors.
Example
Find the acute angle between the lines 3x−5=2y+2=z+1 and ⎝⎛13−5⎠⎞+λ⎝⎛312⎠⎞.
The direction vector of 2x−5=2y+2=z+1 is ⎝⎛321⎠⎞.
Both direction vectors have magnitude
so