Find the distance between the following pairs | vedclass

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Question

(A) The distance between points $P(x_{1}, y_{1}, z_{1})$ and $Q(x_{2}, y_{2}, z_{2})$ is given by the formula:$PQ = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y

Vedclass · Accepted Answer

$2$

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(A) The distance between points $P(x_{1}, y_{1}, z_{1})$ and $Q(x_{2}, y_{2}, z_{2})$ is given by the formula:$PQ = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} + (z_{2}-z_{1})^{2}}$Given points are $(2, 3, 5)$ and $(4, 3, 1)$.Substituting the values into the formula:$PQ = \sqrt{(4-2)^{2} + (3-3)^{2} + (1-5)^{2}}$$PQ = \sqrt{(2)^{2} + (0)^{2} + (-4)^{2}}$$PQ = \sqrt{4 + 0 + 16}$$PQ = \sqrt{20}$$PQ = 2 \sqrt{5}$

Find the distance between the following pairs of points: $(2, 3, 5)$ and $(4, 3, 1)$. (in $\sqrt{5}$)

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