You multiply vectors and scalar simply by multiplying each component by that scalar:

Finally, you sum two vectors by summing the correspondent coordinates:

Answer:
r = -46/3
Step-by-step explanation:
-3(r+2)=40
Distribute
-3r - 6 = 40
Add 6 to each side
-3r-6+6 = 40+6
-3r = 46
Divide by -3
r = 46/-3
r = -46/3
Step-by-step answer:
Referring to the attached diagram, the resultant of two forces each with magnitude F and inclined to each other at 2a equals
Ra = 2Fcos(a) ..............................(1)
Similarly, the resultant of two forces each with magnitude F and inclined to each other at 2b equals
Rb = 2Fcos(b)..............................(2)
We are given that
Ra = 2Rb ....................................(3)
Substitute (1) & (2) in (3) gives
2Fcos(a) = 2(2Fcos(b))
Expand
2Fcos(a) = 4Fcos(b)
Simplify
cos(a) = 2 cos(b) QED
Note: Please note that you might have a faster response if you posted this question in the physics or the (new) Engineering section.
Have a nice day!
Number 3 / last one is -49 hoped I helped you