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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 3.15
Two vector lines are coincident if they represent exactly the same line, meaning every point on one line also lies on the other. For lines given by:
they are coincident if:
Their direction vectors are parallel, so b1=kb2.
A point from one line (e.g., a2) lies on the other line, satisfying a2=a1+λb1 for some scalar λ.
Example
Consider two lines given by:
These lines are coincident because their direction vectors are parallel (one is a scalar multiple of the other), and the point (3,6,9) from the second line lies on the first line (taking λ=1). Thus, both lines represent exactly the same set of points.
AHL 3.15
Two vector lines are coincident if they represent exactly the same line, meaning every point on one line also lies on the other. For lines given by:
they are coincident if:
Their direction vectors are parallel, so b1=kb2.
A point from one line (e.g., a2) lies on the other line, satisfying a2=a1+λb1 for some scalar λ.
Example
Consider two lines given by:
These lines are coincident because their direction vectors are parallel (one is a scalar multiple of the other), and the point (3,6,9) from the second line lies on the first line (taking λ=1). Thus, both lines represent exactly the same set of points.