chetzread said:Homework Statement
Find Parametric equation and vector equation for the portion of parabola y = 1+(x^2) from (1,2) to (2,5)
Homework Equations
The Attempt at a Solution
m = (2-1) i +(5-2)j = i +3j
x = t , y = 1+t^2
r(t) = ti + (2=3t)j, where 0<t<1
, but the ans given is r(t) = ti + (1+t^2) j , 1<t<2
Is my ans acceptable ?
Which part you don't understand ?PeroK said:No. It's not clear to me what you are doing in your solution.
chetzread said:Which part you don't understand ?
My ans is
r(t) = ti + (2=3t)j, where 0<t<1
, but the ans given is r(t) = ti + (1+t^2) j , 1<t<2
My ans isPeroK said:I don't understand any of it. Not least ##(2=3t)j##.
chetzread said:My ans is
r(t) = ti + (2+3t)j, where 0<t<1
, but the ans given is r(t) = ti + (1+t^2) j , 1<t<2
Find a vector equation for the line segment that joins A(1, -1 , 2) and B (4,1,7)PeroK said:For ##t = 0##, you have ##r(0) = 2j##, which is not correct.
Moreover, what you have is a straight line ##y = 3x + 2##. Not a parabola.
chetzread said:Find a vector equation for the line segment that joins A(1, -1 , 2) and B (4,1,7)
My working is :
m = (4-1)i + (1+1 ) j + (7-2)k , so m = 3i + 2j +5k
so , x= 1+2t , y = -1+ 2t z = (2+5t)k
so t = (x-2)/2 = (3-y)/6 = (z+1)/3
So , i use the same concept to do the question in post #1 , is it wrong ? why can't i do so ?
NoPeroK said:Is a parabola a straight line?
chetzread said:No
OkPeroK said:All you are doing is finding the straight line between the end points.
A parametric equation is a set of equations that express the coordinates of a point in terms of one or more parameters, often represented by t. A vector equation is a single equation that represents a vector in terms of its components. In other words, a parametric equation describes the path of a point, while a vector equation represents a single vector.
To convert a parametric equation to a vector equation, you can simply set the parameters equal to the components of a vector. For example, if the parametric equations are x = 2t and y = -3t, the vector equation would be .
Yes, a vector equation can represent a line in three-dimensional space by using three parameters and three corresponding vector components. For example, would represent a line in three-dimensional space.
Parametric equations and vector equations are useful for representing geometric objects, such as lines and curves, in a more compact and efficient way. They also allow for easier manipulation and calculation of these objects.
Yes, a parametric equation or vector equation can have more than one solution. This is because the parameters in the equations can take on different values, resulting in different points or vectors. These equations can also have no solutions if the parameters do not satisfy the given conditions.