What is the correct expression for \vec{OP}?

In summary, the conversation was about a student who missed class on vectors and was now trying to learn it from the book. They were stuck on a problem involving vectors and asked for help expressing certain vectors in terms of given variables. The expert summarizer explains the solution to the problem and helps the student understand their mistake. The student thanks the expert and confirms that they were able to solve the rest of the questions.
  • #1
Argyron
3
0
I missed 2 weeks of class where we were introduced to vectors and now I have to learn it by myself from the book. I'm stuck on this problem that's part of the assigned homework. If anyone could help me that would be great thanks.
I'm sorry if it's a stupid mistake :/

Homework Statement


In triangle OAB, [itex]\vec{OA} = a[/itex] and [itex]\vec{OB} = b[/itex]
P is a point on AB such that [itex]\vec{AP} = 2\vec{PB}[/itex]
and Q is a point such that [itex]\vec{OP} = 3\vec{PQ}[/itex]

Express the following in terms of a and b.
a) [itex]\vec{BA}[/itex]
b) [itex]\vec{PB}[/itex]
c) [itex]\vec{OP}[/itex]
d) [itex]\vec{PQ}[/itex]
e) [itex]\vec{BQ}[/itex]

Homework Equations


N/A

The Attempt at a Solution


a) [itex]\vec{BA} = a-b[/itex]
b) [itex]\vec{PB} = 1/3(b-a)[/itex]

I got stuck on c)
My working out is
[itex]\vec{OP} = \vec{OB} + \vec{BP}[/itex] [Express both vectors in a and b]
[itex]\vec{OP} = b + 1/3(a-b)[/itex]
But when I check my answer the book said it was:
[itex]1/3(a+2b)[/itex]

Where did I go wrong?
 
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  • #2
Argyron said:
I missed 2 weeks of class where we were introduced to vectors and now I have to learn it by myself from the book. I'm stuck on this problem that's part of the assigned homework. If anyone could help me that would be great thanks.
I'm sorry if it's a stupid mistake :/

Homework Statement


In triangle OAB, [itex]\vec{OA} = a[/itex] and [itex]\vec{OB} = b[/itex]
P is a point on AB such that [itex]\vec{AP} = 2\vec{PB}[/itex]
and Q is a point such that [itex]\vec{OP} = 3\vec{PQ}[/itex]

Express the following in terms of a and b.
a) [itex]\vec{BA}[/itex]
b) [itex]\vec{PB}[/itex]
c) [itex]\vec{OP}[/itex]
d) [itex]\vec{PQ}[/itex]
e) [itex]\vec{BQ}[/itex]

Homework Equations


N/A

The Attempt at a Solution


a) [itex]\vec{BA} = a-b[/itex]
b) [itex]\vec{PB} = 1/3(b-a)[/itex]

I got stuck on c)
My working out is
[itex]\vec{OP} = \vec{OB} + \vec{BP}[/itex] [Express both vectors in a and b]
[itex]\vec{OP} = b + 1/3(a-b)[/itex]
But when I check my answer the book said it was:
[itex]1/3(a+2b)[/itex]

Where did I go wrong?

Solve it further.
[tex]\vec{OP} = b + 1/3(a-b)=b+a/3-b/3=a/3+2b/3[/tex]
 
  • #3
Pranav-Arora said:
Solve it further.
[tex]\vec{OP} = b + 1/3(a-b)=b+a/3-b/3=a/3+2b/3[/tex]

That seems so obvious now that I see it. Thanks for that.
 
  • #4
Argyron said:
That seems so obvious now that I see it. Thanks for that.

You are welcome! :smile:

Did you solve the rest of the questions?
 
  • #5
Pranav-Arora said:
You are welcome! :smile:

Did you solve the rest of the questions?

Yeah, it was easy once I had c. :smile:
 

FAQ: What is the correct expression for \vec{OP}?

What is a vector?

A vector is a mathematical entity that has both magnitude (size) and direction. It is commonly represented as an arrow pointing in a specific direction and with a specific length.

What are some common beginner vector problems?

Some common beginner vector problems include finding the resultant vector (sum) of two or more vectors, finding the components of a vector, and finding the angle between two vectors.

How do I add or subtract vectors?

To add or subtract vectors, you need to break them down into their components (horizontal and vertical) and then add or subtract the components separately. The resulting vector will have a magnitude and direction that can be found using the Pythagorean theorem and trigonometric functions.

What is the difference between a scalar and a vector?

A scalar is a mathematical entity that has only magnitude (size) and no direction, whereas a vector has both magnitude and direction. Scalars are represented by a single number, while vectors are represented by an arrow.

How can I apply vectors in real life?

Vectors have various applications in real life, such as in physics, engineering, navigation, and computer graphics. For example, vectors are used to represent forces in physics, to calculate the displacement of an object, and to create 3D animations in computer graphics.

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