The components of a vector V can be written (Vx, Vy, Vz).?

Question

What are the components and length of a vector which is the sum of the two vectors, V1 and V2, whose components are (2.2, 2.0, 0.0) and (4.9, -4.1, -0.4)

components (____),(____),(_____).

Length (____)

I can get the components but the lenght will not come out for me

Answer 1

For components, I get (7.1,-2.1,-0.4).

To find the resultant of these, you can use Pythagorus.

Start just considering the x and y axes.

Vx^2 + Vy^2 = Vr^2
where Vr is the resultant of the x and y components.

Now consider Vz along with Vr. These 2 are perpendicular. To picture this, get a small box and label one corner the origin and the 3 edges extending from the origin x, y, and z axes. You can draw Vr on the face that is the xy plane. (Just imagine the length of the sides of your box is the length of our Vx, Vy, and Vz. So Vr is corner to corner on that face.) Now if you can imagine inside the box, the z axis is perpendicular to Vr.

So you can use Pythagorus again, on Vz and Vr.
Vz^2 + Vr^2 = length^2
Now substitute for Vr^2
Vz^2 + Vx^2 + Vy^2 = length^2