Question

With respect to a rectangular Cartesian coordinate system, three vectors are expressed as
`vec(a)= 4hat(i)-hat(j), vec(b)= -3hat(i)+2hat(j) and vec(c )= -hat(k)`
Where, `hat(i), hat(j), hat(k)` are unit Vector, along the X, Y and Z-axis respectively. The unit vectors `hat(r )` along the direction of sum of these vector is
A. `vec(r )= 1/(sqrt(3))(hat(i)+hat(j)-hat(k))`
B. `vec(r )= 1/(sqrt(2))(hat(i)+hat(j)-hat(k))`
C. `vec(r )= 1/3(hat(i)-hat(j)+hat(k))`
D. `vec(r )= 1/(sqrt(2))(hat(i)+hat(j)+hat(k))`

Answer 1

Correct Answer - A
`vec(r )= vec(a)+vec(b)+vec(c )= 4hat(i)-hat(j)-3hat(i)+2hat(j)-hat(k)= hat(i)+hat(j)-hat(k)`
`vec(r )=(vec(r))/(|vec(r)|)=(hat(i)+hat(j)-hat(k))/(sqrt(1^(2)+1^(2)+(-1)^(2)))=(hat(i)+hat(j)-hat(k))/(sqrt(3))`