Question

The unit vector parallel to the resultant of the vectors `vec(A)= 4hat(i)+3hat(j)+6hat(k)` and `vec(B)= -hat(i)+3hat(j)-8hat(k)` is
A. `1/7(3hat(i)+6hat(j)-2hat(k))`
B. `1/7(3hat(i)+6hat(j)+2hat(k))`
C. `1/(49)(3hat(i)+6hat(j)-2hat(k))`
D. `1/(49)(3hat(i)-6hat(j)+2hat(k))`

Answer 1

Correct Answer - A
Resutant of vectors `vec(A)` and `vec(B)`
`vec(R )= vec(A)+vec(B)= 4hat(i)+3hat(j)+6hat(k)-hat(i)+3hat(j)-8hat(k)`
`vec(R )= 3hat(i)+6hat(j)-2hat(k)`
`hat(R )= (vec(R ))/(|vec(R )|)= (3hat(i)+6hat(j)-2hat(k))/(sqrt(3^(2)+6^(2)+(-2)^(2)))= (3hat(i)+6hat(j)-2hat(k))/7`