# Magnitude of Hiker's Vectors A, B & C

• triplel777
In summary, the hiker's route consisted of three displacement vectors: A, B, and C. Vector A was 1550 m in magnitude and had a direction of 28.0° north of east. Vector B was not along a measured trail, but the hiker used a compass and determined its direction to be 41.0° east of south. Vector C had a direction of 12.0° north of west. The resultant displacement was zero, meaning A + B + C = 0. By drawing a triangle and using the law of sines, the magnitudes of vector B and vector C were found to be approximately -1138.78 m and 635.99 m, respectively.
triplel777

## Homework Statement

The route followed by a hiker consists of three displacement vectors A, B, and C. Vector A is along a measured trail and is 1550 m in a direction 28.0° north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 41.0° east of south. Similarly, the direction of vector is 12.0° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or A + B + C = 0. Find the magnitudes of vector B and vector C.

## The Attempt at a Solution

i drew the triangle. broke it into two equations with two unknowns in each.
x: 1550cos28+bcos311 + ccos168=0
y: 1550sin28+bsin311+csin168=0
which gave me b= -1138.78 and c= 635.99

Last edited:

What are the three angles of your triangle? Hint: Try using the law of sines.

i drew the triangle. broke it into two equations with two unknowns in each.
x: 1550cos28+bcos311 + ccos168=0
y: 1550sin28+bsin311+csin168=0
which gave me b= -1138.78 and c= 635.99

and what about the angles they give in the problem?

Your two starting equations are correct, but you numbers are not. Redo the calculation. If you still get the same numbers, then you must show how you got them so that we can help you. Don't forget to set your calculator to "Degree" mode.

triplel777 said:
i drew the triangle.
If you drew the closed triangle A-B-C and you figured out its angles, then you could use the law of sines to solve for the two unknown sides.

broke it into two equations with two unknowns in each.
x: 1550cos28+bcos311 + ccos168=0
y: 1550sin28+bsin311+csin168=0
which gave me b= -1138.78 and c= 635.99
As kuruman said, your equations for the components are fine, but the solution is not.

and what about the angles they give in the problem?
What about them? Presumably you used them to find the angles that you used in your equations. You could also use them to figure out the angles in the triangle.

## 1. What is the magnitude of a vector?

The magnitude of a vector is its size or length. It is calculated using the Pythagorean theorem, which involves finding the square root of the sum of the squares of the vector's components.

## 2. How is the magnitude of a vector represented?

The magnitude of a vector is typically represented by using absolute value notation, such as |A| or ||A||. It can also be represented by using the vector's symbol with a bar over it, such as |A| or ||A||.

## 3. What is the significance of the magnitude of a vector in hiking?

The magnitude of a vector in hiking represents the distance and direction of a hiker's movement. It is important to know the magnitude of a hiker's vectors A, B, and C to understand their overall displacement and the total distance they have traveled.

## 4. How is the magnitude of a vector calculated in hiking?

In hiking, the magnitude of a vector is calculated by using the hiker's coordinates at the starting point and ending point of their journey. These coordinates are used to find the distance between the two points, which is then used as the magnitude of the vector.

## 5. Can the magnitude of a vector be negative?

No, the magnitude of a vector cannot be negative. It is always a positive value that represents the length or size of the vector. However, the direction of the vector can be negative, which indicates movement in the opposite direction of the positive direction.

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