Find the vector that must be added to the vector `hat(i)-3hat(j)+2hat(k)` and `3hat(i)+6hat(j)-7hat(k)` so that the resultant vector is a unit vector along the y-axis.

Options

A. `4hat(i)+ 2hat(j)+ 5hat(k)`
B. `-4 hat(i)- 2hat(j) + 5hat(k)`
C. `3hat(i) + 4hat(j)+ 5 hat(k)`
D. Null vector

Answer

B

Explanation

Unit vector along Y axis `= hat(j)` Then required vector `= hat(j) - [(hat(i)- 3 hat(j)+ 2hat(k)) + (3hat(i) + 6hat(j) - 7hat(k))]`
`= -4hat(i)- 2hat(j)+ 5 vec(k)`