Find sets of parametric equations and symmetric equations of the line that passes through the two points (if possible). (For each line, write the direction numbers as integers.) (0, 0, 25), (10, 10, 0)

a)Parametric equations are

X= -10t

Y= -10t and

z= 25+25t

b) Symmetric equations are

(x/-10) = (y/-10) = (z- 25)/25

Step-by-step 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

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