1)

A=3i^ - 4j^ +5k^,B=2i^ +3j^ -4k^

R=A+B

  =(3+2)i^ +(-4+3)j^ +(5-4)k^

  =5i^ - j^ + k^

A+B=5i^ - j^ + k^

the magnitude of R=(5)²+(-1)²+(1)²

                           =27

                           =33

unit vector parallel to (A+B)=(5i^ - j^ + k^)/33 

 

2)

A₁=x₁i^ + y₁j^ + z₁k^

A₂=x₂i^ + y₂j^ + z₂k^

for these vectors to be parallel to each other

x₁/x₂=y₁/y₂=z₁/z₂

 

A₁=2i^ + 3j^ - 4k^

A₂=3i^ - aj^ + bk^

 

2/3=3/(-a)

-a=9/2

a=-4.5

 

2/3=-4/b

b=-12/2

b=-6

 

the second vector must be 3i^ +4.5j^ -6k^ for the two vectors to be parallel