what is difference between component and magnitude of vector?is it possible for the magnitude equal to the value of component?when could this occur?
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I find the other answers quite confusing, and to calm my nerves I must write a superfluous response.
Consider the definition of magnitude, which involves squaring both components, adding them, and taking the square root of this sum.
Sound familiar?
In algebra we know the Pythagorean theorem, which relates the sides of a right triangle by the same formula that relates components to magnitude.
So, a and b are components and c is the magnitude.
Coming back to the question, we will use casework to find a solution.
1. Both components are larger than the magnitude, making the answer "yes"
We know that squares are always positive, and adding two positive numbers will only result in a larger positive number that is greater than each individual component, so this relation is false
2. One component is larger than the magnitude
Consider the inequality,
a > (a^2 + b^2)^1/2
Since all numbers in the equation are positive we can square to get
a^2 > a^2 + b^2
Subtract a^2
0 > b^2,
A contradiction since b^2 must at least be equal to zero.
QED, the answer is no
Consider the definition of magnitude, which involves squaring both components, adding them, and taking the square root of this sum.
Sound familiar?
In algebra we know the Pythagorean theorem, which relates the sides of a right triangle by the same formula that relates components to magnitude.
So, a and b are components and c is the magnitude.
Coming back to the question, we will use casework to find a solution.
1. Both components are larger than the magnitude, making the answer "yes"
We know that squares are always positive, and adding two positive numbers will only result in a larger positive number that is greater than each individual component, so this relation is false
2. One component is larger than the magnitude
Consider the inequality,
a > (a^2 + b^2)^1/2
Since all numbers in the equation are positive we can square to get
a^2 > a^2 + b^2
Subtract a^2
0 > b^2,
A contradiction since b^2 must at least be equal to zero.
QED, the answer is no
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COMPONENTS = Component's Components describe the changes in the x- and y- axes.
At y- axis v sin € is the component( vertical) to obtain value and at x - axis v cos € is the component ( horizontal)
MAGNITUDE = It is equal to the hypotenuse of the right triangle obtained after drawing vertical and horizontal components.
It is possible for the magnitude to be equal to the value of component. It will occur when both cancel out each other.
At y- axis v sin € is the component( vertical) to obtain value and at x - axis v cos € is the component ( horizontal)
MAGNITUDE = It is equal to the hypotenuse of the right triangle obtained after drawing vertical and horizontal components.
It is possible for the magnitude to be equal to the value of component. It will occur when both cancel out each other.
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