1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Allushta [10]
3 years ago
11

Find the equation for the plane that contains the line x=−1+3t , y=1+2t, z=2+4t and is perpendicular to the plane containing the

two lines
L1: x=2t+1,y=-t-1,z=6t+5

L2:x=t+1,y=t-1,z=-3t+5
Mathematics
1 answer:
Ivan3 years ago
8 0

Let L be the line given by the vector equation

(-1,1,2) + \lambda(3,2,4) \ , \lambda \in \mathbb{R}.

First, we use the director vectors of the lines L1 and L2 to get the

vector equation of the plane containing them, which we denote by \Pi_1. This is,

\\\\\Pi_1  : (1,-1,5) + \alpha (2,-1,6) + \beta (1,1,-3) \ , \alpha, \beta \in \mathbb{R}\\\\\\

We observe that \vec{N} = (2,-1,6)\times(1,1,-3) = (-3,12,3) \ne (0,0,0). Therefore, the vector equation of \Pi_1 defines a plane and \vec{N} is a normal vector to \Pi_1.

 

Finally, the vector equation for the wanted plane, which we denote by \Pi, is

\Pi : (-1,1,2) + r(3,2,4) + s(-3,12,3), r,s \in \mathbb{R} \ .

Thus, if s = 0, then L \subset \Pi and since \vec{N} is parallel to \Pi, then it is perpendicular to \Pi_1.

You might be interested in
Selma is about to purchase a new television that is listed for $415.99. If sales tax is 7.75%, what
Alex787 [66]

Answer:

448.23

Step-by-step explanation:

Sales tax is addition to the original price

The original price is 100%

First we find 1% of this, which is 415.99 / 100 = 4.1599

Then multiply this by 7.75 = 32.239225

Add this to the original price = 415.99 + 32.239225 = 448.229225

You have to round this to an appropriate number as the question uses two decimal places I think this will suffice = 448.23

6 0
3 years ago
(a) A color printer prints 11 pages in 7 minutes. How many pages does it print per minute?
umka21 [38]
Hello there.

<span>(a) A color printer prints 11 pages in 7 minutes. How many pages does it print per minute? 
(b) It takes 63 pounds of seed to completely plant an 8 -acre field. How many acres can be planted per pound of seed?

Answer:
A) 11/7 = 1.6
B) 8/63 = 0.13.

Hope This Helps You!
Good Luck Studying ^-^</span>
8 0
3 years ago
Read 2 more answers
Prove that PQ + QR + RS + SP = 0 in the given quadrilateral<br>PQRS.​
earnstyle [38]

Answer:

PDRS

Step-by-step explanation:

PQ IS EQUAL TO QR AND QR IS ALSO EQUAL TO RS AND RS IS ALSO EQUAL TO SP

4 0
2 years ago
Read 2 more answers
Parametric test based on standard error ​
Delvig [45]

Answer:

The parametric hypothesis tests that we introduced in Chapter 5 were all based upon the means of the sample and population.

8 0
2 years ago
Sonji plots -9 on a number line to represent the depth of her sailboat underwater and labels it B. She plots positive 20
AfilCa [17]

Answer: the answer ould be b hope this helps could you brainliest plz

Step-by-step explanation:

well bc one of the number on the cordinate plane is a negative and the other is a positive than it would be answer choice b hope this helps and could you PLZ brainliest please

8 0
3 years ago
Other questions:
  • After basketball practice, Courtney spent extra time working on free throws. Overall, she made 3 of her 5 shots. What percent of
    12·2 answers
  • What is 372 divided by 2
    12·2 answers
  • |3n – 6| = 6<br> absolute value equation
    5·1 answer
  • What is 40 times 103
    8·2 answers
  • 10q - 20 is equivalent to _____
    5·2 answers
  • Please help with c d and e
    15·1 answer
  • Find the value of x and y. Triangle MNP = triangle TUS
    7·1 answer
  • For a polynomial p(x), if p(a) = 0, then which of the following must be a factor of p(x)?
    11·1 answer
  • When Justin was born, he was 45.7 cm long. Now he is
    6·1 answer
  • Construct a triangle ABC if AB = 4 cm, BC = 5 cm and Y = 30 °, then enter a circle​
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!