Answer:
a)Parametric equations are
X= -10t
Y= -10t and
z= 25+25t
b) Symmetric equations are
(x/-10) = (y/-10) = (z- 25)/25
Explanation:
We were told to fin two things here which are ; a) the parametric equations and b) the symmetric equations
The given two points are (0, 0, 25)and (10, 10, 0)
The direction vector from the points (0, 0, 25) and (10, 10, 0)
(a,b,c) =( 0 -10 , 0-10 ,25-0)
= < -10 , -10 ,25>
The direction vector is
(a,b,c) = < -10 , -10 ,25>
The parametric equations passing through the point (X₁,Y₁,Z₁)and parallel to the direction vector (a,b,c) are X= x₁+ at ,y=y₁+by ,z=z₁+ct
Substitute (X₁ ,Y₁ ,Z₁)= (0, 0, 25), and (a,b,c) = < -10 , -10 ,25>
and in parametric equations.
Parametric equations are X= 0-10t
Y= 0-10t and z= 25+25t
Therefore, the Parametric equations are
X= -10t
Y= -10t and
z= 25+25t
b) Symmetric equations:
If the direction numbers image and image are all non zero, then eliminate the parameter image to obtain symmetric equations of the line.
(x-x₁)/a = (y-y₁)/b = (z-z₁)/c
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION