Given that OA = 3i – 2j + k and OB = 4i – j – 3k. Find the distance between points A and B to 2 decimal places.
Well, to find the distance between points A and B, we can use the distance formula. Remember it? It's like a math road trip!
So the distance (d) between two points, let's say A and B, is given by the formula:
d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)
In this case, we have:
A = (3, -2, 1) and B = (4, -1, -3)
So let's calculate the distance:
d = √((4 - 3)² + (-1 - (-2))² + (-3 - 1)²)
d = √(1² + 1² + (-4)²)
d = √(1 + 1 + 16)
d = √18
And when we round that to two decimal places, we get approximately 4.24.
So, the distance between points A and B is about 4.24. And remember, no road trip is complete without snacks!