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:$d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_

Vedclass · Accepted Answer

$2 \sqrt{26}$

Vedclass · Answer

(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:$d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} + (z_{2}-z_{1})^{2}}$Given points are $P(-1, 3, -4)$ and $Q(1, -3, 4)$.Substituting the values into the formula:$d = \sqrt{(1 - (-1))^{2} + (-3 - 3)^{2} + (4 - (-4))^{2}}$$d = \sqrt{(1 + 1)^{2} + (-6)^{2} + (4 + 4)^{2}}$$d = \sqrt{(2)^{2} + (-6)^{2} + (8)^{2}}$$d = \sqrt{4 + 36 + 64}$$d = \sqrt{104}$$d = \sqrt{4 	imes 26} = 2 \sqrt{26}$

Find the distance between the following pairs of points: $(-1, 3, -4)$ and $(1, -3, 4)$.

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