If A=(7.4,-3) and B(-4,457), find ||AB||. Round to 3 decimal place

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26-10-2022
Mathematics

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If A=(7.4,-3) and B(-4,457), find ||AB||. Round to 3 decimal place

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ListonM483742 ListonM483742 · Answer 1 · 2022-10-26T13:37:49+02:00

If A = (7, 4, -3) and B = (-4, 4, 7) represented by (x, y, z), it is 3- dimensional.

[tex]\parallel AB\parallel\text{ =}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2_{}}[/tex][tex]\begin{gathered} \parallel AB\parallel=\sqrt[]{(-4_{}-7_{})^2+(4_{}-4)^2+(7_{}-(-3)_{})^2_{}} \\ \parallel AB\parallel=\sqrt[]{(-11_{})^2+(0)^2+(10)^2_{}} \\ \parallel AB\parallel=\sqrt[]{121^{}+0^2+100} \\ \parallel AB\parallel=\sqrt[]{221} \\ \parallel AB\parallel=\text{ 14.866 (to 3 decimal places)} \end{gathered}[/tex]

Therefore, the norm is 14.866 to 3 decimal places.