The vector 2i^−j^−2k^ has the desired direction. To find a vector in the same direction with magnitude 9 units, the original vector needs to be scaled appropriately.
The magnitude of 2i^−j^−2k^ is:
∣vector∣=(2)2+(−1)2+(−2)2
=4+1+4
=9
=3 units
To scale the vector to magnitude 9 units, multiply by the ratio of desired magnitude to current magnitude:
Scaling factor =39=3
Required vector =3(2i^−j^−2k^)
=6i^−3j^−6k^
Therefore, the vector in the direction of 2i^−j^−2k^ with magnitude 9 units is 6i^−3j^−6k^.