Symmetric equations of a line are (x-1)/2 = (y+2)/-3 = (z-4)/5. Determine vector and parametric equations for the line.
Is this right?
v = < 2, -3, 5 >
Parametric Equations:
x = 1 + 2t
y = -2 - 3t
z = 4 + 5t
Looks good to me.
Yes, you are correct! The vector equation for the line in question is:
r = <x, y, z> = <1, -2, 4> + t<2, -3, 5>
Where t is a parameter that represents different points along the line.
To convert this vector equation into parametric equations, we simply equate each component of the vector equation to a corresponding variable equation:
x = 1 + 2t
y = -2 - 3t
z = 4 + 5t
These are the parametric equations for the line. They represent the x, y, and z coordinates of any point on the line in terms of the parameter t.