Does this line lie in this plane?

• jegues
Therefore, the two expressions are not equivalent and the line does not lie in the plane.In summary, the problem statement is asking if a given line lies in a given plane. The solution involves translating the line into parametric equations and substituting them into the plane's equation. After simplifying, the solutions manual states that 9t-1 does not equal -1, which means the line does not lie in the plane. This is because for the entire line to lie in the plane, the equation would have to be true for all values of t, not just t=0.
jegues

Homework Statement

See figure for problem statement. It asks if a given line lies in a given plane.

The Attempt at a Solution

Okay so first I translated the line into its parametric equations and then I subbed those into the equation of the plane respectively.

After simplifying you'll find that,

$$9t-1 = -1$$

Now my solutions manual states the following,

*NOTE* There is no symbol for not-equivalent in tex, so I'm writing NE

$$9t -1 NE -1$$

Why is this so?

Why not let t = 0, and then -1 = -1 and then all will be well in world, no?

What am I missing?

Attachments

• LIP.jpg
27.8 KB · Views: 430
jegues said:
*NOTE* There is no symbol for not-equivalent in tex, so I'm writing NE

\neq works

$$9t -1 \neq -1$$

Why is this so?

Why not let t = 0, and then -1 = -1 and then all will be well in world, no?

What am I missing?

Each value of $t$ corresponds to a single point on the line. If the entire line were to lie in the plane, the equation would have to be true for all values of $t$ (all points on the line), not just $t=0$

1. What is the definition of a line?

A line is a straight path that extends infinitely in both directions.

2. How is a line represented mathematically?

A line can be represented using the slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.

3. What is the definition of a plane?

A plane is a flat, two-dimensional surface that extends infinitely in all directions.

4. How is a plane represented mathematically?

A plane can be represented using the equation Ax + By + Cz + D = 0, where A, B, and C are the coefficients of the variables x, y, and z, and D is a constant.

5. How do you determine if a line lies in a plane?

A line lies in a plane if all of its points are also points of the plane. This means that the line's equation must satisfy the equation of the plane, or in other words, the line's coordinates must satisfy the plane's equation when substituted in for x, y, and z.

• Calculus and Beyond Homework Help
Replies
3
Views
1K
• Calculus and Beyond Homework Help
Replies
5
Views
2K
• Calculus and Beyond Homework Help
Replies
6
Views
3K
• Calculus and Beyond Homework Help
Replies
9
Views
1K
• Calculus and Beyond Homework Help
Replies
9
Views
2K
• Calculus and Beyond Homework Help
Replies
2
Views
1K
• Calculus and Beyond Homework Help
Replies
11
Views
1K
• Calculus and Beyond Homework Help
Replies
5
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
2K
• Calculus and Beyond Homework Help
Replies
5
Views
1K