Question

A unit vector in the dirction of resultant vector of `vec(A)= -2hat(i)+3hat(j)+hat(k)` and `vec(B)= hat(i)+2hat(j)-4hat(k)` is
A. `(-2hat(i)+3hat(j)+hat(k))/(sqrt(35))`
B. `(-hat(i)+2hat(j)+4hat(k))/(sqrt(35))`
C. `(-hat(i)+5hat(j)-3hat(k))/(sqrt(35))`
D. `(-3hat(i)+hat(j)-5hat(k))/(sqrt(35))`

Answer 1

Correct Answer - C
Here, `vec(A)= -2hat(i)+3hat(j)+hat(k)`
`vec(B)= hat(i)+2hat(j)-4hat(k)`
The resultant vector of `vec(A)` and `vec(B)` is
`vec(R )= vec(A)+vec(B)= (2hat(i)+3hat(j)+hat(k))+(hat(i)+2hat(j)-4hat(k))`
`= -hat(i)+5hat(j)-3hat(k)`
`|vec(R )= sqrt((-1)^(2)+(5)^(2)+(-3)^(2))= sqrt(1+25+9)= sqrt(35)`
Unit vector in the direction of resultant vector of `vec(A)` and `vec(B)` is
`hat(R )= (vec(R ))/(|R|)= (-hat(i)+5hat(j)-3hat(k))/(sqrt(35))`