what is the magnitude of a vector with an initial point (2,6) and a terminal point (14,11)
d^2 = (y2-y1)^2 + (x2-x1)^2
d^2 = 5^2 + 12^2 = 13^2
(5 12 13 right triangle)
13
Well, hang onto your funny bone because I'm about to clown around with some numbers. The magnitude of a vector can be found using the good ol' Pythagorean theorem. So, let's get this ridiculous calculation started, shall we?
First, we need to find the differences between the x-coordinates and y-coordinates of the initial and terminal points. So, subtracting the x-coordinates, we get 14 - 2 = 12. And subtracting the y-coordinates gives us 11 - 6 = 5.
Now, let's square these differences. Squaring 12 gives us a whopping 144, while squaring 5 gives us a tiny 25 (I told you this was going to be funny!).
Next, we need to add these squares together. 144 + 25 equals 169.
Finally, we take the square root of 169 to get the magnitude.
Drumroll, please... (ba-dum-tss)
The magnitude of this vector is the square root of 169, which is 13.
So, the magnitude of the vector with an initial point (2,6) and a terminal point (14,11) is 13. Tada!
To find the magnitude of a vector, you can use the distance formula. The magnitude of a vector is the same as the length of the line segment connecting its initial point to its terminal point.
The distance formula is given by the equation:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the initial and terminal points of the vector, respectively.
In this case, the initial point is (2, 6) and the terminal point is (14, 11). Therefore, substituting these values into the distance formula, we have:
d = √((14 - 2)^2 + (11 - 6)^2)
Simplifying further:
d = √(12^2 + 5^2)
= √(144 + 25)
= √(169)
= 13
Therefore, the magnitude of the vector with an initial point (2, 6) and a terminal point (14, 11) is 13.
To find the magnitude of a vector with an initial point (2,6) and a terminal point (14,11), we can use the distance formula.
The distance formula is derived from the Pythagorean theorem, and it allows us to find the distance between two points in a coordinate plane. In this case, we can treat the vector as a straight line connecting the initial and terminal points.
The formula for finding the distance between two points (x₁, y₁) and (x₂, y₂) is:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
So, let's substitute the coordinates of the initial point and the terminal point into the formula:
distance = √((14 - 2)² + (11 - 6)²)
= √(12² + 5²)
= √(144 + 25)
= √169
= 13
Therefore, the magnitude of the vector is 13.