Find a vector that has the same direction as −2, 6, 4 but has length 6.

To find a vector that has the same direction as −2, 6, 4 but has length 6, we can follow these steps:

1. Calculate the magnitude of the given vector: magnitude = √((-2)^2 + 6^2 + 4^2) = √(4 + 36 + 16) = √56 = 2√14

2. Divide each component of the given vector by its magnitude to obtain the unit vector: unit vector = (-2/2√14, 6/2√14, 4/2√14) = (-√14/√14, 3√14/√14, 2√14/√14) = (-1/√14, 3/√14, 2/√14)

3. Multiply each component of the unit vector by the desired length (6) to obtain the final vector: final vector = (6*(-1/√14), 6*(3/√14), 6*(2/√14)) = (-6/√14, 18/√14, 12/√14)

Therefore, a vector that has the same direction as −2, 6, 4 but has length 6 is approximately (-0.45, 1.34, 0.89).