Question

What is the distance between `(7,9,4)` and `(3,-5,1)`?

Answer 1

`L = sqrt((x_2-x_1)^2 +(y_2-y_1)^2+(z_2-z_1)^2)`

I will let you finish this.

Explanation:

`color(blue)("Step 1")`

`color(brown)("First consider the horizontal plane of x,y")`

The image of strait line between these point can be projected onto the x,y plane. This, when considered in relation to the axis forms a triangle.

So you can determine the length of the projection on that plane by using Pythagoras.

`color(blue)("Step 2")`

`color(brown)("You now consider the z-axis.")`

The image on the xy plane is considered as the adjacent of a triangle and the z-axis as the opposite. Again you can use Pythagoras. This time the result is the actual magnitude of the distance between the points.

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Let L be the length of the strait line between the points.

Then `L = sqrt((x_2-x_1)^2 +(y_2-y_1)^2+(z_2-z_1)^2)`

I will let you work that out!