A vector has a component of 10 in the +x direction, a component of 10 in the +y direction, and a component of 5 in the -z direction. The magnitude of this vector is:Group of answer choices2250152025
Question
A vector has a component of 10 in the +x direction, a component of 10 in the +y direction, and a component of 5 in the -z direction. The magnitude of this vector is:Group of answer choices2250152025
Solution
The magnitude of a vector is calculated using the Pythagorean theorem, which in three dimensions is:
Magnitude = sqrt((x^2) + (y^2) + (z^2))
Here, x = 10, y = 10, and z = -5.
So,
Magnitude = sqrt((10^2) + (10^2) + ((-5)^2)) Magnitude = sqrt((100) + (100) + (25)) Magnitude = sqrt(225)
Therefore, the magnitude of the vector is 15.
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