What is the unit vector parallel to ` vec a=3 hat i+4 hat j-2 hat k` ? What vector should be added to ` vec a` so that the resultant is the unit vector ` hat i ?`

Explanation

We have `veca= 3hati + 4hatj - 2hatk `. Therefore,
`" "|veca| = sqrt(9+ 16 + 4) = sqrt(29)`
Therefore, the unit vector parallel to
`" " a = (veca) /(|veca|) = (1)/(sqrt((29)))= (3hati + 4hatj - 2hatk )`.
Now suppose `vecb` is the vector which when added to `veca` gives the resultant `hati`. Then
`veca + vecb = hati or vecb = hati - veca = hati - (3hati + 4hatj - 2hatk)`
`therefore vecb = -2hati - 4hatj +2hatk`