Determine the vector u = AB and its magnitude, given A(3,7,-2) and B(9,1,5).
u = [9-3,1-7,5+2] = [6,-6,7]
|u| = √(36+36+49) = √121 = 11
thankyou!
To determine the vector u = AB, we can subtract the coordinates of A from the coordinates of B.
The vector u = AB is given by:
u = B - A
To obtain the coordinates of u, subtract the corresponding coordinates of A and B:
u = (9, 1, 5) - (3, 7, -2)
= (9 - 3, 1 - 7, 5 - (-2))
= (6, -6, 7)
The magnitude of vector u can be calculated using the formula:
|u| = √(x^2 + y^2 + z^2)
where (x, y, z) are the components of the vector. In this case, (6, -6, 7).
|u| = √(6^2 + (-6)^2 + 7^2)
= √(36 + 36 + 49)
= √121
= 11
Therefore, the vector u = (6, -6, 7) and its magnitude is 11.