If the x-component of a vector is 3 and the y-component is 4, what is the magnitude of the vector?

To find the magnitude of a vector given its components, you can use the Pythagorean theorem. The formula for the magnitude ( V ) of a vector with components ( x ) and ( y ) is expressed as:

[

V = \sqrt{x^2 + y^2}

]

In this scenario, the x-component of the vector is 3 and the y-component is 4. Plugging these values into the formula yields:

[

V = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5

]

Thus, the magnitude of the vector is 5. This calculation is fundamental in physics, as it relates to finding the resultant length of a vector in two-dimensional space.