Determine a vector which when added to the resultant of `vec(A)= 2hat(i)+5hat(j)-hat(k)` and `vec(B)= 3hat(i)-4hat(j)-hat(k)` gives unit Vector along negative y direction.

Options

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

Answer

A

Explanation

Let `vec(C )`is required Vector, then `vec(C )+vec(A)+vec(B)= -hat(j)`
`implies vec(C )+2hat(i)+5hat(j)-hat(k)+3hat(i)-4hat(j)-hat(k)= -hat(j)`
`implies vec(C )= -5hat(i)-2hat(j)+2hat(k)`