Question

If A=17,4,-3) and B(-4,4,7), find ||AB||. Round to 3 decimal places.Type your answer...

Answer 1

14.866

Explanation

the distance between two points is given by:

$\begin{gathered} D_{12}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \\ where \\ P1(x_1,y_1,z_1)andP2(x_2,y_2,z_2) \end{gathered}$

then

Step 1

Let

P1=A(7,4,-3)

P2=B=(-4,4,7)

Now, replace

$\begin{gathered} D_{12}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \\ D_{AB}=\sqrt[]{(-4-7)^2+(4-4)^2+(7-(-3))^2} \\ D_{AB}=\sqrt[]{(-11)^2+(0)^2+(10)^2} \\ D_{AB}=\sqrt[]{121+0+100} \\ D_{AB}=\sqrt[]{221} \\ D_{AB}=14.86 \end{gathered}$

Step 2

Now, let's round to the decimal places.

$14.866061\rightarrow14.866$

so, the answer is 14.866

I hope this helps you