Final answer:
To obtain a vector of length 21 in the same direction as [2,3,6], scale the components of the original vector by 3 to get [6,9,18].
Step-by-step explanation:
To find the components for a vector of length 21 that points in the same direction as [2,3,6], we need to scale the original vector so that its magnitude is 21 while preserving its direction.
First, we find the magnitude of the given vector [2,3,6] using the Pythagorean theorem:
Magnitude = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7
Since the desired length of the vector is 21, which is 3 times the original vector's magnitude, we multiply each component of the vector [2,3,6] by 3 to get the components of the new vector:
- x-component = 2 × 3 = 6
- y-component = 3 × 3 = 9
- z-component = 6 × 3 = 18
Therefore, the components of the new vector are [6,9,18].