Question

Please help as soon as possible This is grade 12 math vectors

Answer 1

Answer:

48*sqrt(2)

Let me know if there was anything you didn't understand

Step-by-step explanation:

To find the distance between any two points on a normal 2D graph you would  use the pythagorean theorem.  Well, if you have a 3D graph  you do something similar, where instead of just two dimensions it is 3.  so you take the sum of the length squared, width squared and height squared and they equal this 3D hypotenuse.

So, AB is the distance between A and B.    so you take the x distance, y distance and z distance to find the height, length and width.  The two points are (4, 0, 0) and (6, 3, 5).

Startign witht he x coordinates the difference is 2, since there are 2 between 4and 6.

y then is the difference between 0 and 3, so just 3

z then of course is 5.

so now to find AB you do that 3D pythagorean theorem.

AB = sqrt(2^2 + 3^2 + 5^2)  = sqrt(36) = 6

BC is the distance between points (6,3, 5) and (2,3,5) so now the x distance is 4, y is 0 and z is 0.  so then BC = sqrt(4^2 + 0^2 + 0^2) = 4

Finally BD is sqrt(0^2 + 2^2 + 2^2) = sqrt(8)

Then just multiply all those together 6*4*sqrt(8) = 24*sqrt(8) = 48*sqrt(2)  i simplified sqrt(8) into sqrt(4*2) = sqrt(4) * sqrt(2) = 2*sqrt(2).  Simplifying is just the standard thing you are supposed to do.