Question
A point in three-dimensional space can be represented in a three-dimensional coordinate system. In such a case, a $z$ -axis is taken perpendicular to both the $x$ - and $y$ -axes. A point $A$ is assigned an ordered triple $A(x, y, z)$ relative to a fixed origin where the three axes meet. For Exercises $91-94$, determine the distance between the two given points in space. Use the distance formula$d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}+\left(z_{2}-z_{1}\right)^{2}}$.(3,7,-2) and (0,-5,1)
Step 1
We have $A(3,7,-2)$ and $B(0,-5,1)$. So, $x_1 = 3$, $y_1 = 7$, $z_1 = -2$, $x_2 = 0$, $y_2 = -5$, and $z_2 = 1$. Show more…
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A point in three-dimensional space can be represented in a three-dimensional coordinate system. In such a case, a $z$ -axis is taken perpendicular to both the $x$ - and $y$ -axes. A point $A$ is assigned an ordered triple $A(x, y, z)$ relative to a fixed origin where the three axes meet. For Exercises $91-94$, determine the distance between the two given points in space. Use the distance formula $d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}+\left(z_{2}-z_{1}\right)^{2}}$. (5,-3,2) and (4,6,-1)
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A point in three-dimensional space can be represented in a three-dimensional coordinate system. In such a case, a $z$ -axis is taken perpendicular to both the $x$ - and $y$ -axes. A point $A$ is assigned an ordered triple $A(x, y, z)$ relative to a fixed origin where the three axes meet. For Exercises $91-94$, determine the distance between the two given points in space. Use the distance formula $d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}+\left(z_{2}-z_{1}\right)^{2}}$. (6,-4,-1) and (2,3,1)
A point in three-dimensional space can be represented in a three-dimensional coordinate system. In such a case, a $z$ -axis is taken perpendicular to both the $x$ - and $y$ -axes. A point $A$ is assigned an ordered triple $A(x, y, z)$ relative to a fixed origin where the three axes meet. For Exercises $91-94$, determine the distance between the two given points in space. Use the distance formula $d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}+\left(z_{2}-z_{1}\right)^{2}}$. (9,-5,-3) and (2,0,1)
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