Question

three forces (and no others) act upon an object, which remains at rest. the forces are represented by the vectors P, Q and R where P=-4i-5j and Q=-2i+9j. find the magnitude and direction of the vector

the answer options i got are magnitude 3.2 or magnitude 7.2 and the options i got for direction are -146.3 degrees. -56.3 degrees, -33.7 degrees, 33.7 degrees, 56.3 degrees or 146.3 degrees

Answer 1

"Remains at rest" always always always means:

"Summation of the forces is going to amount to zero"

Answer 2

Sum P and Q.
R will equal that sum times -1
As the total sum will be 0 a stated by brinethery.

Answer 3

how do you tell the direction though

Answer 4

R will be 180 degrees from the sum of P and Q

Answer 5

the answer options i got are magnitude 3.2 or magnitude 7.2 and the options i got for direction are -146.3 degrees. -56.3 degrees, -33.7 degrees, 33.7 degrees, 56.3 degrees or 146.3 degrees

Answer 6

well, since P + Q will give you -6i + 4j, R will be 6i-4j, so with this, you can calculate the magnitude with pythagoras, and the angle with tan(4/6)

Answer 7

how would pythagoras work as you dont have the side, sorry but im totally lost here

Answer 8

Now, you know the components of the vector R, as radar stated, it's 180 opposite from P+Q. Since you already have the vector components, you can draw a right triangle and calculate everything with it. Do you see it?