Final answer:
To find the unit vector in direction of ω = 0i + 16j, divide by its magnitude, which is 16, giving the unit vector j.
Step-by-step explanation:
The question asks how to find the unit vector in the direction of the vector ω = 0i + 16j. To find the unit vector, we divide the given vector by its magnitude. The magnitude of ω can be calculated using the Pythagorean theorem, which for this vector simplifies to the absolute value of its j-component since the i-component is zero. Therefore, the magnitude is equal to the absolute value of 16, which is 16. Dividing each component of ω by 16 gives us the unit vector in the direction of ω: (0/16)i + (16/16)j = 0i + 1j, often simply written as j. This unit vector represents the positive direction on the y-axis, according to the standard Cartesian coordinate system. The use of unit vectors is crucial for expressing vectors in a standardized form where the direction is clearly identified by the unit vector, and the magnitude signifies how much of that direction the vector embodies.