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

Answer

B

Explanation

Unit vector along y axis `=hat(j)`. So the required vector,
`=hat(j) - [(hat(i)-3hat(j)+2hat(k))+(3hat(i)+6hat(j)-7hat(k))]= -4hat(i)-2hat(j)+5hat(k)`