Given three vectors A = (1, 1, 1), B = (-1, 2, 3) and C = (0, 3, 4), find the unit vector in the direction of A+B – C.
To find the unit vector in the direction of A + B - C, we need to first find the vector A + B - C and then normalize it.
Adding the three vectors, we get:
A + B - C = (1, 1, 1) + (-1, 2, 3) - (0, 3, 4)
= (1, 1, 1) - (1, 2, 3)
= (1 - 1, 1 - 2, 1 - 3)
= (0, -1, -2)
To normalize this vector, we divide each component by its magnitude:
Magnitude of (0, -1, -2) = sqrt(0^2 + (-1)^2 + (-2)^2) = sqrt(0 + 1 + 4) = sqrt(5)
So, the unit vector in the direction of A + B - C is:
(0, -1, -2) / sqrt(5)
To find the unit vector in the direction of A+B-C, we need to follow these steps:
1. Calculate the vector A + B - C:
A + B - C = (1, 1, 1) + (-1, 2, 3) - (0, 3, 4)
= (1 - 1 - 0, 1 + 2 - 3, 1 + 3 - 4)
= (0, 0, 0)
2. Calculate the magnitude of the vector A + B - C:
||A + B - C|| = sqrt(0^2 + 0^2 + 0^2)
= sqrt(0)
= 0
3. Divide the vector A + B - C by its magnitude to obtain the unit vector:
Unit vector = (0, 0, 0) / 0
= Undefined
Therefore, the unit vector in the direction of A+B–C is undefined because the magnitude of the vector A+B–C is zero.