Determine the magnitude of the positive vectors from the origin to to the following points.
A. (3,4)
B. (12,5)
C. (3,-2)
D. (-7,-3)
Okay, what point is your origin? Normally it is (0,0) but not always...
yes its zero
To determine the magnitude of the vectors from the origin to the given points, we can use the formula for calculating the magnitude of a 2D vector. The formula is:
Magnitude (or length) = √(x^2 + y^2)
Now let's calculate the magnitudes of the given vectors:
A. To determine the magnitude of the vector (3,4), we substitute the values into the formula:
Magnitude of A = √(3^2 + 4^2)
= √(9 + 16)
= √25
= 5
So, the magnitude of vector A is 5.
B. For the vector (12,5), we use the same formula:
Magnitude of B = √(12^2 + 5^2)
= √(144 + 25)
= √169
= 13
Thus, the magnitude of vector B is 13.
C. To find the magnitude of the vector (3,-2):
Magnitude of C = √(3^2 + (-2)^2)
= √(9 + 4)
= √13
Therefore, the magnitude of vector C is √13.
D. Lastly, we'll find the magnitude of the vector (-7,-3):
Magnitude of D = √((-7)^2 + (-3)^2)
= √(49 + 9)
= √58
So, the magnitude of vector D is √58.