Answer:
![2\sqrt6](https://tex.z-dn.net/?f=2%5Csqrt6)
Step-by-step explanation:
We have been given that the dot product if u with itself is 24.
Now, we know that the dot product of vector a and b is given by
![a\cdot b=|a||b|\cos\theta](https://tex.z-dn.net/?f=a%5Ccdot%20b%3D%7Ca%7C%7Cb%7C%5Ccos%5Ctheta)
Here,
is the angle between the vectors a and b.
We have to find the dot product of u with itself. Hence,
a = u
b = u
Thus, dot product is given by
![u\cdot u=|u||u|\cos0\\\\24=|u||u|\cdot1\\\\|u|^2=24\\\\|u|=2\sqrt6](https://tex.z-dn.net/?f=u%5Ccdot%20u%3D%7Cu%7C%7Cu%7C%5Ccos0%5C%5C%5C%5C24%3D%7Cu%7C%7Cu%7C%5Ccdot1%5C%5C%5C%5C%7Cu%7C%5E2%3D24%5C%5C%5C%5C%7Cu%7C%3D2%5Csqrt6)
Thus, the magnitude of u is ![2\sqrt6](https://tex.z-dn.net/?f=2%5Csqrt6)