Question

The vector that must be added to the vector i-3j+2k and 3i+6j-7k so that the resultant vector is a unit vector along the x axis

Answer 1

The unit vector along x-axis is i.

So (i-3j+2k) + (3i+6j-7k) + (xi+yj+zk) = i
Vector addition or subtraction is just adding/subtracting magnitudes in corresponding axes.

(1+3+x)i + (-3+6+y)j + (2-7+z)k = i

1+3+x = 1
x = -3

-3+6+y = 0
y = -3

2-7+z=0
z=5

Therefore the vector is -3i-3j+5k