salinasroel22
06.07.2019 •
Mathematics
Find parametric equations for the line through the point (0, 3, 2) that is parallel to the plane x + y + z = 5 and perpendicular to the line x = 1 + t, y = 3 − t, z = 2t. (use the parameter t.)
Solved
Show answers
More tips
- F Food and Cooking The Disease That Haunted Abraham Lincoln...
- P Philosophy What is Something for you?...
- S Style and Beauty Intimate Haircut: The Reasons, Popularity, and Risks...
- A Art and Culture When Will Eurovision 2011 Take Place?...
- S Style and Beauty How to Choose the Perfect Hair Straightener?...
- F Family and Home Why Having Pets at Home is Good for Your Health...
- H Health and Medicine How to perform artificial respiration?...
- H Health and Medicine 10 Tips for Avoiding Vitamin Deficiency...
- F Food and Cooking How to Properly Cook Buckwheat?...
- F Food and Cooking How Many Grams Are In a Tablespoon?...
Answers on questions: Mathematics
- M Mathematics Which statement is true about the graphed function? O Fx) 0 over the interval (-0, 4) OFx) 0 over the interval (-0, -3) O F(x) 0 over the interval (-00, -3) O F(x) 0 over the interval...
- M Mathematics The velocity of a free-falling object is given by V = V2gh where h is the distance (in feet) the object has fallen and g is acceleration due to gravity (in feet per second squared)....
- M Mathematics A baby furniture store has a number of different dressers. The table below shows the number of dressers and their heights. Which histogram matches the table?...
- M Mathematics A jet aircraft maintains a constant airspeed of 500 miles per hour in the direction due south. The velocity of jet stream is 80 miles per hour in a northeasterly direction. Find...
- M Mathematics A company makes 140 bags 30 of the bags buttons but no zips. 27 of the bags have zips but no buttons. 20 of the bags have neither zips or buttons. How many bags have zips on them...
- M Mathematics cool/3d18c3ab-98a2-4989-9e70-1d62f58e3bcf/Showitem?returnView=&studentItemid=0&backPath Question 3 of 17 A room has dimensions 10 6 X 14 . What is the perimeter of the room?...
- M Mathematics The total distance jim traveled on his bicycle during a 5 hour period is shown in the graph below....
- M Mathematics Write an algebraic expression to model the unknown number situation. the sum of five and a number Complete each statement to explain how to model this situation. Replace “a number”...
- M Mathematics Solve -6 + 8 = 12. Can y’all plz help...
- M Mathematics Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Kaitlyn is interviewing applicants for an open job position in her...
Ответ:
let A(0,3,2) and (Δ) this line , v vector parallel to (Δ).
M∈ (Δ) : vector (AM) = t v t ∈ R
1 ) (Δ) parallel to the plane x + y + z = 5 : let : n an vector perpendicular
to the plane : n ⊥ v n(1,1,1) so : n.v =0 means : n.vector (AM) = 0
(1)(x)+(1)(y-3)+(1)(z -2) =0 ( vector (AM) = ( x, y -3 , z-2 )
x+y+z - 5=0 ...(1)
2) (Δ) perpendicular to the line (Δ') : x = 1+t , y = 3 - t , z = 2t :
vector (u) ⊥ v vector(u) parallel to (Δ') and vector(u) = (1 , -1 ,1)
vector (u) ⊥ vector (AM) means :
(1)(x)+(-1)(y-3)+(2)(z -2) =0
x - y+2z - 1 = 0 ...(2)
so the system :
x+y+z - 5=0 ...(1)
x - y+2z - 1 = 0 ...(2)
(1)+(2) : 2x+3z - 6 =0
x = 3 - (3/2)z
subsct in (1) : 3 - (3/2)z +y +z - 5 =0
y = 1/2z +2
let : z=t
an parametric equations for the line (Δ) is : x = 3 - (3/2)t
y = (1/2)t +2
z=t
verifiy :
1) (Δ) parallel to the plane x + y + z = 5 :
(-3/2 , 1/2 ,1) perpendicular to (1,1,1)
because : (1)(-3/2)+(1)(1/2)+(1)(1) = -1 +1 = 0
2) (Δ) perpendicular to the line (Δ') :
(-3/2 , 1/2 ,1) perpendicular to (1,-1,2)
because : (1)(-3/2)+(-1)(1/2)+(1)(2) = -2 +2 = 0
A(0, 3, 2)∈(Δ) :
0 = 3-(3/2)t
3 = (1/2)t+2
2 =t
same : t = 2
Ответ: