# Prove the following lines are perpendicular.

I am not understanding how to follow through on this exercise, so if someone could explain it to me I would appreciate it.

r:

x + y - 3z - 1 = 0

2x - y - 9z - 2 = 0

is perpendicular to

s:

2x + y + z + 5 = 0

2x - 2y - z + 2 = 0

and the second part requires me to prove

r:

2x + y − 4z + 2 = 0

4x − y − 5z + 4 = 0

is perpendicular to

s:

x = 1 + 2λ

y = −2 + 3λ

z = 1 − 6λ

I apologize for the bad formatting, I wasn't sure how else I could arrange the equations. Thanks for any help.

• Do you require that the lines intersect for them to be perpendicular? – amd Apr 28 '18 at 0:42
• See the help center for information about how to format equations. – Simply Beautiful Art Apr 28 '18 at 12:49

The direction vector of $\mathbb{r}$ is given by $(\vec{i}+\vec{j}-3\vec{k})\times(2\vec{i}-\vec{j}-9\vec{k})$. You can find the direction vector of $\mathbb{s}$ by cross product in a similar way.
You can find the direction vector of $\mathbb{r}$ by cross product. The direction vector of $\mathbb{s}$ is $2\vec{i}+3\vec{j}-6\vec{k}$.
The text passage contains two separate exercises asking to prove that pairs of lines are perpendicular. Each exercise provides the equations of the lines and asks for a proof of perpendicularity.
multiple_questions_with_answers

the passage contains multiple questions (two exercises asking to prove perpendicularity), and answers or guidance for solving these questions are provided in the form of direction vectors and methods to find them.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Prove the following lines are perpendicular.

I am not understanding how to follow through on this exercise, so if someone could explain it to me I would appreciate it.

r:

x + y - 3z - 1 = 0

2x - y - 9z - 2 = 0

is perpendicular to

s:

2x + y + z + 5 = 0

2x - 2y - z + 2 = 0

and the second part requires me to prove

r:

2x + y − 4z + 2 = 0

4x − y − 5z + 4 = 0

is perpendicular to

s:

x = 1 + 2λ

y = −2 + 3λ

z = 1 − 6λ

I apologize for the bad formatting, I wasn't sure how else I could arrange the equations. Thanks for any help.

• Do you require that the lines intersect for them to be perpendicular? – amd Apr 28 '18 at 0:42
• See the help center for information about how to format equations. – Simply Beautiful Art Apr 28 '18 at 12:49

The direction vector of $\mathbb{r}$ is given by $(\vec{i}+\vec{j}-3\vec{k})\times(2\vec{i}-\vec{j}-9\vec{k})$. You can find the direction vector of $\mathbb{s}$ by cross product in a similar way.
You can find the direction vector of $\mathbb{r}$ by cross product. The direction vector of $\mathbb{s}$ is $2\vec{i}+3\vec{j}-6\vec{k}$.
user
The text passage contains two separate exercises asking to prove that pairs of lines are perpendicular. Each exercise provides the equations of the lines and asks for a proof of perpendicularity.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS

The passage contains multiple questions (two exercises asking to prove perpendicularity), and answers or guidance for solving these questions are provided in the form of direction vectors and methods to find them.