Question

7. (-/1 Points) DETAILS LARCALC11 11.R.037. Find sets of parametric equations and symmetric equations of the line that passes through the two points. (For the line, write the direction numbers as integers.) (7, 0,5), (10, 11, 9) (a) Find sets of parametric equations. (Enter your answer as a comma-separated list of equations in terms of x, y, z, and t.) (b) Find sets of symmetric equations. *57 - 11 3+5 0 - 7x + 3 = 11y = -5z + 4 O 3x + 7 = 11y = 4z + 5 O -.'; ܐ 8. [-/1 Points) DETAILS LARCALC11 11.R.040. Find a set of parametric equations of the line with the given characteristics. (Enter your answer as a comma-separated list of equations in terms of x, y, z, and t.) The line passes through the point (1, 4, 2) and is parallel to the line given by x = y = z.

Answer 1

• The vector equation of a line that passes through the points  
  (20, Yo, 20)
  and
  (Iz 'th 10)
  is given by :

r=ro + tū

To
is the point vector of initial point

t - is a parameter

ບ.
is a vector parallel to the vector formed by two points

= [20 - 21]{+ [yo – yı]] + [zo – zik

12 - 02 Th 02 'Tfi – Of Ir of Ir – 0.1

T= 20, Yo, 20) + (20 – 21, yo – 41, 20 – 21

• The parametric equation of line is given by

if:7 →
be any arbitrary point such that :
(zh) = 1

(12 – 0z Th – Of Tr – 02) 7 + (Oz oh oz) = (zh)

(2, 4, 2) (:20, Yo, 20) + (t [10 - 21], tyo - y1], [20 – 21])

(2, 4, 2) = (20 +t (20 - 11],yo+t (yo - y1], 20+t [20 – 21

>> I= co +t Co - 11

> y = yo +t yo – Yi

>> 2= 20 +t [20 – 21

• The symmetric form of the equation is
• 
  Do +tico – 21
  

T1 0.0 0.0

• 
  y = yo +t yo – Y1
  

Y - Yo Yo — Yi =t

• 
  z = 20 + t20 – 21
  

Oz t 20 21

Thjerefore :

0.0 Y Yo - 20 Ir – 01 Yo — Y1 20 – 21

Given :

Two points ( 7 , 0 , 5 ) and ( 10 , 11 , 9 )

20.yo, 20) = (7,0,5)

6 'IT'OI) = (Tz th )

The parametric equations is given by :

• 
  Do +tico – 21
  

  
= 7+t(7 – 10

r= 7 - 3t

• 
  y = yo +t yo – Y1
  

= 0 + (0 – 11)

y -11t

• 
  z = 20 + t20 – 21
  

  
= 5 + +(5-9)

=5- 46

The parametric equations are:

T 7 – 31

-117

2=5 - 41

The symmetric form of equation is given by:

r= 7 - 3t

.2 - 7 t -3

y -11t

=t -11

=5- 46

t

Therefore :

- 7 2 =] y -11 2-5 5 -4 -3

Multiping whole equation by -1

y - یا 11 ته