convert these symmetric equations to parametric form:
line 1:(x-1)/k = (y-2)/2 = (z+1)/k-1
and
line 2: (x+3)/-2 = (z)/1, y=-1
To convert symmetric equations to parametric form, we can assign variables to each term and solve for them. Let's start with line 1:
(x - 1) / k = (y - 2) / 2 = (z + 1) / (k - 1)
We can assign the variable "t" as a parameter, then write x, y, and z in terms of "t":
x = 1 + kt
y = 2 + 2t
z = -1 + (k - 1)t
Now, let's convert line 2:
(x + 3) / -2 = z / 1
y = -1
Similarly, let's assign the variable "s" as a parameter:
x = -3 - 2s
y = -1
z = s
Now we have parametric form representations of the given symmetric equations:
For line 1:
x = 1 + kt
y = 2 + 2t
z = -1 + (k - 1)t
For line 2:
x = -3 - 2s
y = -1
z = s