If `vec(A)=4hat(i)-3hat(j)` and `vec(B)=6hat(i)+8hat(j)`,then find the magnitude and direction of `vec(A)+vec(B)`.

Options

A. `5, tan^(-1) (3//4)`
B. `5 sqrt5, tan^(-1) (1//2)`
C. `10, tan^(-1) (5)`
D. `25, tan^(-1) (3//4)`

Answer

B

Explanation

`vec(A) + vec(B) = 4hat(i) - 3hat(j) + 6hat(i) + 8 hat(j)= 10 hat(i) + 5hat(j)`
Magnitude `- |vec(A) + vec(B)|= sqrt(10^(2) + 5^(2))= sqrt125 = 5 sqrt5`
`tan theta= (5)/(10) rArr theta= tan^(-1) (1//2)`