find unit vector in the same directions as the vectors: (-3 6 4)
that would be (-3 6 4)/√61
To find the unit vector in the same direction as a given vector, you need to divide each component of the vector by its magnitude.
Let's find the magnitude of the vector (-3, 6, 4):
Magnitude = sqrt((-3)^2 + 6^2 + 4^2)
= sqrt(9 + 36 + 16)
= sqrt(61)
Now, divide each component of the vector by its magnitude:
Unit vector = ((-3 / sqrt(61)), (6 / sqrt(61)), (4 / sqrt(61)))
Therefore, the unit vector in the same direction as the vector (-3, 6, 4) is approximately:
(-0.389, 0.778, 0.519)
To find the unit vector in the same direction as a given vector, follow these steps:
Step 1: Calculate the magnitude of the vector.
- To calculate the magnitude of a 3D vector, use the formula: |v| = √(x^2 + y^2 + z^2), where (x, y, z) are the coordinates of the vector.
For the given vector (-3, 6, 4):
- |v| = √((-3)^2 + 6^2 + 4^2) = √(9 + 36 + 16) = √61
Step 2: Divide each component of the vector by its magnitude.
- To find the unit vector, divide each component of the vector by its magnitude.
- The unit vector will have the same direction as the original vector but with a magnitude of 1.
For the given vector (-3, 6, 4):
- (u1, u2, u3) = (-3/√61, 6/√61, 4/√61)
Therefore, the unit vector in the same direction as the vector (-3, 6, 4) is approximately:
(u1, u2, u3) ≈ (-0.387, 0.774, 0.516)