Oh no! We're facing turbulence quick to the command deck!
Welcome aboard the spaceship the USS Calamari!
(60000km/h [N] + 10000km/h [S]) = 50000km/h [N]
Our spaceship heading north at an air speed of 60000 km/h and the spaceship is encountering a resistance north at 10000km/h, what is the resultant ground velocity of the ship?
(60000km/h [N] + 10000km/h [N]) = 70000km/h [N]
Oh no! There is a resistance from the south at 100km/h, what is the resultant ground velocity of the ship?
(1,1,0) x (1,0,1) = (1,-1,-1) |(1,-1,1-)| = √1^2+(-1)^2+(-1)^2 = √3
Thank god! We can now recalculate how long it will take to get to our destination… Uh, oh, the engine of the spaceship is a flat parallelogram and needs urgent repair. Discover it’s area if it has been formed by the following vectors: (1, 1, 0) and (1, 0, 1)
Find a point on line 1 where you will get your x, y, z Use the A, B, C, D on line 2 Plug the numbers into the formulas d = |Ax + By + Cz + D|/root A^2 + B^2 + C^2 You will get 21/64 units
Great! The engine is now repaired thanks to your quick thinking… Now we need to see how long it will take to travel to this other plane. What is the distance between the planes (1) x - y +z + 3 = 0 and (2) -4x + 4y - 4z + 9 = 0.
Got it! We are almost at our destination thanks to you!