Problem on vector length
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Find the length of the vector from $(2,4,5)$ to $(3, -1, -2)$.
Solution
First we find the vector from $(2,4,5)$ to $(3,-1,-2)$. Then, we compute it's length.
Recall that
Subtraction gives the vector between two points
The vector from $\mathbf{x}$ to $\mathbf{y}$ is given by $\mathbf{y} - \mathbf{x}$.
The vector from $(2,4,5)$ to $(3, -1, -2)$ is thus $$(3,-1,-2) -(2,4,5) = (1, -5, -7).$$
Recall that
Definition of vector length
The length of the vector $\mathbf{z} = (z_1, z_2, z_3 )$ is $ \sqrt{z_1^2 + z_2^2 + z_3^2}.$
The length of the vector from $(2,4,5)$ to $(3, -1, -2)$ is thus $$\sqrt{1^2 + (-5)^2 + (-7)^2} = \sqrt{75}.$$
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