# Solve Problem w/ Vectors Forces of Magnitude 3,5,7 N | x Component 4.968

• MMCS
In summary, the user defined function str2mat converts a string representation of a vector into a Mathcad array. The over-arrow is the vectorize operator which converts the vector into a two-dimensional array.
MMCS
Question

Forces of magnitude 3 Newtons, 5 Newtons and 7 Newtons act along the vectors (-3,-2,-9) (8,5,-9) (4,-1,-9)

Find the x component.

I have the answer at 4.968 however i can not arrive at it, attached is my working out. d has been used instead of c.i have the x components as 2.531, -2.774 and -6.93 however these are not correct as they do not equal the answer of 4.968

**Im pretty sure the figures are correct, there is most probably error in the method

Thanks

#### Attachments

• Working.jpg
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Last edited:
Normalize the given vectors to unit length.

Is that not what i have done.For example, on F1 i have divided it by the magnitude of AB (13.038) then multiplied it by the magnitude of Newtons given in the question (3N) ?

I don't know why you chose to multiply the vectors together first - there was no need.

I didnt multiply them, it isn't clear from the working out sorry, where it says ab it represents the vector a to b.

Ah. The three triplets are the vectors - the forces act from the origin towards those coordinates.

Does the following help?

Notes:
• str2mat is user-defined function that converts a string representation of a vector into a Mathcad array
• the over-arrow is the vectorize operator (you probably know this, but ...)

#### Attachments

• phys - 13 01 07 force vectors 01.JPG
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Im only new to mathcad so i wasnt aware of them functions but ill give them a go they look to solve the problem pretty easily thanks!

I recommend solving this without Mathcad, to get a feel for the process. Your initial problem with solution was not associated with Mathcad use, but with understanding what was specified in the problem.

NemoReally said:
Does the following help?

Notes:
• str2mat is user-defined function that converts a string representation of a vector into a Mathcad array
• the over-arrow is the vectorize operator (you probably know this, but ...)

Please do not do student's homework for them here on the PF. That is against our rules here.

Instead, give hints, ask questions, find errors in their work, etc. We need to have the students doing the bulk of their schoolwork themselves.

## 1. What is the formula for calculating the magnitude of a vector?

The magnitude of a vector can be calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squared components. In this case, the magnitude would be equal to √(3² + 5² + 7²) = √83 ≈ 9.11 N.

## 2. How do I find the x-component of a vector?

To find the x-component of a vector, you can use the formula x = magnitude * cos(θ), where θ is the angle between the vector and the x-axis. In this case, the x-component would be equal to 9.11 N * cos(4.968°) ≈ 8.97 N.

## 3. What is the difference between a scalar and a vector?

A scalar is a physical quantity that only has magnitude, while a vector is a physical quantity that has both magnitude and direction. In this problem, the forces of 3, 5, and 7 N are scalars, while the x-component of the vector is a vector since it has both magnitude and direction.

## 4. How do I solve a problem with multiple vector forces?

To solve a problem with multiple vector forces, you can use vector addition. This involves breaking down each vector into its x and y components, adding the components separately, and then combining them back into a vector using the Pythagorean theorem. In this case, the x-component of the vector can be added to the other forces to find the net force in the x-direction.

## 5. Can vectors be negative?

Yes, vectors can have negative components. This indicates the direction of the vector. In this problem, the x-component of the vector is positive, but if it were negative, it would indicate that the force is acting in the opposite direction of the positive x-axis.

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