# Calculus and Vectors - Vector and Parametric Equations

• ttpp1124
In summary, we discussed finding the values of t that correspond to points P and Q in a parametric equation and a vector equation. We also discussed how to check the correctness of the equations by substituting values for t and performing vector addition. It is important to check your work when solving problems.
ttpp1124
Homework Statement
Calculus and Vectors - Vector and Parametric Equations
I solved it, can someone concur?
Relevant Equations
Not Available

-

For the parametric equation, what are the values of ##t## corresponding to the points ##P## and ##Q## that you were given?

Same for the vector equation. ##t = 0## gives you ##P##. What value of ##t## gives you ##Q##?

That's always a good check.

When I sub in 0 for t, I get the values corresponding to the direction vector. That's how I know it's correct

ttpp1124 said:
When I sub in 0 for t, I get the values corresponding to the direction vector. That's how I know it's correct

Looks wrong to me!

PeroK said:
Looks wrong to me!
how is it wrong?

ttpp1124 said:
how is it wrong?
Is that ##x = -2t, \ y = -1 + 3t, \ z = 6 + 5t##?

PeroK said:
Is that ##x = -2t, \ y = -1 + 3t, \ z = 6 + 5t##?
Yes

ttpp1124 said:
Yes
That's not right. What values of ##t## give you ##P## and ##Q##?

PeroK said:
That's not right. What values of ##t## give you ##P## and ##Q##?
Is it the direction vector, 0,-1,6?

ttpp1124 said:
Is it the direction vector, 0,-1,6?
The vector equation is correct. That's the direction ##\vec{QP}##.

PeroK said:
The vector equation is correct. That's the direction ##\vec{QP}##.
Right, so I think I didn't multiply the t value and do vector addition. When I do multiply, I get r = (-2,3,5)+(0t,-t,6t).
Then I do vector addition by components, so then my parametric equations should be -2+0t, 3-t, and 5+6t

ttpp1124 said:
Right, so I think I didn't multiply the t value and do vector addition. When I do multiply, I get r = (-2,3,5)+(0t,-t,6t).
Then I do vector addition by components, so then my parametric equations should be -2+0t, 3-t, and 5+6t
So, what value of ##t## gives you ##Q##?

PeroK said:
So, what value of ##t## gives you ##Q##?
-1

PeroK
ttpp1124 said:
-1
My question is, how does the value of t have anything to do with the actual question? They just wanted to know the vector and parametric equations.

My question is, how does the value of t have anything to do with the actual question? They just wanted to know the vector and parametric equations.

Also, are my new parametric equations correct?

ttpp1124 said:
My question is, how does the value of t have anything to do with the actual question? They just wanted to know the vector and parametric equations.

Also, are my new parametric equations correct?

## What is a vector in calculus and how is it represented?

A vector in calculus is a mathematical object that has both magnitude (size) and direction. It is commonly represented by an arrow with a length and a direction. In parametric equations, a vector is represented by two or three components, depending on whether it is in two or three dimensions.

## What are parametric equations and how are they used in calculus?

Parametric equations are a set of equations that express the coordinates of a point in terms of one or more independent variables, called parameters. They are used in calculus to describe the motion of a point or object in space, and to find the derivatives and integrals of vector functions.

## How do you find the derivative of a vector function?

To find the derivative of a vector function, you can use the chain rule. First, find the derivative of each component of the vector function with respect to the independent variable. Then, combine these derivatives to form a new vector, which is the derivative of the original vector function.

## What is the dot product of two vectors and how is it calculated?

The dot product of two vectors is a scalar quantity that represents the projection of one vector onto the other. It is calculated by multiplying the magnitudes of the two vectors and the cosine of the angle between them.

## What is the cross product of two vectors and how is it calculated?

The cross product of two vectors is a vector that is perpendicular to both of the original vectors. It is calculated by taking the determinant of a 3x3 matrix formed by the components of the two vectors. The magnitude of the cross product is equal to the product of the magnitudes of the two vectors and the sine of the angle between them.

• Calculus and Beyond Homework Help
Replies
2
Views
784
• Calculus and Beyond Homework Help
Replies
4
Views
2K
• Calculus and Beyond Homework Help
Replies
7
Views
1K
• Calculus and Beyond Homework Help
Replies
10
Views
1K
• Calculus and Beyond Homework Help
Replies
4
Views
1K
• Calculus and Beyond Homework Help
Replies
6
Views
888
• Calculus and Beyond Homework Help
Replies
23
Views
2K
• Calculus and Beyond Homework Help
Replies
5
Views
1K
• Calculus and Beyond Homework Help
Replies
1
Views
1K
• Calculus and Beyond Homework Help
Replies
2
Views
1K