Vector equation of a straight line (HSC SSCE Mathematics Extension 2): Flashcards
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What is the vector equation of a straight line?
What is the vector equation of a straight line?
r = r0 + λv, with r0 as a point and v as a direction vector.
What does the direction vector v indicate?
What does the direction vector v indicate?
It shows the line's orientation in space.
How is the parametric form of a line written?
How is the parametric form of a line written?
x = x0 + aλ, y = y0 + bλ, z = z0 + cλ.
What are the conditions for lines to be parallel?
What are the conditions for lines to be parallel?
Direction vectors are scalar multiples of each other.
When are lines perpendicular?
When are lines perpendicular?
Their direction vectors' dot product equals zero.
What is the first step to find the intersection point?
What is the first step to find the intersection point?
Set parametric equations equal and solve for parameters.
How do you verify the intersection point?
How do you verify the intersection point?
Substitute parameters into equations to check consistency.
Why are vector equations crucial in 3D geometry?
Why are vector equations crucial in 3D geometry?
They describe lines precisely with vectors.
Vector equation of a line in 3D?
Vector equation of a line in 3D?
r = r0 + λv; r0 is point, v is direction
When are two lines parallel?
When are two lines parallel?
Their direction vectors are scalar multiples.