Final answer:
To find a vector of magnitude 3 in the direction of v=15i-20k, first, normalize the given vector by dividing each component of the vector by its magnitude to create a unit vector with the same direction. Then, multiply the unit vector by the desired magnitude of 3.
Step-by-step explanation:
To find a vector of magnitude 3 in the direction of v=15i-20k, we first need to normalize the given vector. Normalizing a vector involves dividing each component of the vector by its magnitude to create a unit vector with the same direction.
The magnitude of v=15i-20k can be found using the Pythagorean theorem: |v| = sqrt((15)^2 + (-20)^2) = 25. The unit vector in the direction of v is then u = (15/25)i + (-20/25)k = 0.6i - 0.8k.
Multiplying the unit vector u by the desired magnitude of 3 gives us the vector of magnitude 3 in the direction of v: 3u = 3(0.6i - 0.8k) = 1.8i - 2.4k.