Solving problems involving operations on vectors

Two like parallel forces of 4N and 8N are 15m apart. Find the distance in meters of the line of action of their resultant from 4N force.

• 10m
• 25m
• 20m
• 5m

Simplify

• A
• B
• C
• D

u=<-6,-8> , v=<2,5> . Find Find 3u+4v

• <10,4>

• <-10,-4>

• <-18,24>

• <-26,-44>

Three vectors are shown in Figure 1. Their magnitudes are given in arbitrary units. Find the magnitude of the resultant vector.

• 26.70

• 27.06

• 13.50

• 50

Calculate 2a + c

• 
• 
• 
• 

Calculate a+c-b

• 
• 
• 

• c₁ =2 , c₂ =-2

• c₁ =2 , c₂ =-3

• c₁ =1 , c₂ =2

• c₁ =-1 , c₂ =3

An airplane is flying in the direction S60⁰W with airspeed of 450 mph. It encounters a 65 mph wind in the direction of S25⁰E. What are the resultant speed and direction of the plane?

• W38.088⁰S at 460.243 mph

• W68.291⁰S at 449.029 mph

• W218.088⁰N at 458.264 mph

• W47.048⁰S at 432.741 mph

The vectors have magnitudes of 17 and 28 and the angle between them is 66°. Determine the magnitude of the resultant.

Give your answer to 1 decimal place, leave out the units.