Calculating magnitudes of vectors

In summary, a vector is a mathematical quantity with both magnitude and direction, represented by an arrow. Its magnitude is calculated using the Pythagorean theorem, and it cannot be negative. The magnitude and direction are both necessary to fully describe a vector. In three dimensions, the magnitude is calculated by adding an additional component to the Pythagorean theorem.
  • #1
PAstudent
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Vector picture.png

1. Homework Statement

Given the two vectors in the diagram, calculate their magnitudes if A+B-225j=0

Homework Equations


sum of x component= Acos(42)--Bcos(56)
sum of y component= Asin(42)+Bsin(56)--225j

The Attempt at a Solution


Find A and B use substitution

A= [Bcos(56)]/cos(42) from x comp.

plug that into y comp. to solve for B

[Bcos(56)sin(42)]/cos(42) + Bsin(56) -- 225j=0

After solving, I got B= 168.85 and A=127.05. Does that seem correct?
 
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  • #2
I haven't checked your arithmetic, but your setup of the equations looks correct...except for those j's in the y component equations.

Chet
 

1. What is a vector?

A vector is a mathematical quantity that has both magnitude (size or length) and direction. It is represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow indicating the direction of the vector.

2. How do you calculate the magnitude of a vector?

The magnitude of a vector is calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the other two sides. In the case of a vector, the magnitude is equal to the square root of the sum of the squares of its components. For example, if a vector has components of 3 and 4, its magnitude would be calculated as √(3² + 4²) = √25 = 5.

3. What is the difference between magnitude and direction?

Magnitude refers to the size or length of a vector, while direction refers to the angle or orientation of the vector. Both magnitude and direction are necessary to fully describe a vector.

4. Can the magnitude of a vector be negative?

No, the magnitude of a vector is always a positive value. It represents the length or size of the vector, which cannot be negative.

5. How do you calculate the magnitude of a vector in three dimensions?

The magnitude of a vector in three dimensions is calculated using the same method as in two dimensions, but with an additional component added to account for the third dimension. The magnitude is equal to the square root of the sum of the squares of all three components. For example, if a vector has components of 2, 3, and 4, its magnitude would be calculated as √(2² + 3² + 4²) = √29 ≈ 5.39.

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