Vector AB is a vector whose tail is at (-4,2) and whose head is at (-1,3).
Calculate the magnitude of vector AB
Determine the coordinates of point D on vector CD, if C (-6,0) and vector CD= vector AB.
Please I need some help. Is there a formula to solve this? Pls help
Yes, there are formulas to solve both parts of your question. Let's go through them step by step.
1. Calculating the magnitude of vector AB:
The magnitude of a vector can be calculated using the distance formula, which is derived from the Pythagorean theorem.
The formula for the magnitude or length (|AB|) of vector AB with coordinates (x1, y1) and (x2, y2) is:
|AB| = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can calculate the magnitude of vector AB as follows:
x1 = -4, y1 = 2
x2 = -1, y2 = 3
|AB| = sqrt((-1 - (-4))^2 + (3 - 2)^2)
= sqrt(3^2 + 1^2)
= sqrt(9 + 1)
= sqrt(10)
Therefore, the magnitude of vector AB is sqrt(10).
2. Determining the coordinates of point D on vector CD:
If vector CD is equal to vector AB, then the coordinates of point D will be the same as the coordinates of point B.
From the given information, we know that point B has coordinates (-1, 3). Therefore, the coordinates of point D on vector CD will also be (-1, 3).
I hope this explanation helps you understand how to solve these types of problems. Let me know if you have any further questions!