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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

Mathematics
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"Remains at rest" always always always means: "Summation of the forces is going to amount to zero"
Sum P and Q. R will equal that sum times -1 As the total sum will be 0 a stated by brinethery.
how do you tell the direction though

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R will be 180 degrees from the sum of P and Q
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
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)
how would pythagoras work as you dont have the side, sorry but im totally lost here
|dw:1334598901478:dw| 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?
|dw:1334599135199:dw|
i kinda see where you are coming from but i still cant see what i have got to put on each side cos i just got letters so how do i get a number degrees out of it or a magnitude
i and j are unit vectors, which means that their length is 1. For the purpose of this, it's simply a triangle with sides 4 and 6. the angle can then easily be found, it's tan^-1(4/6) and you adjust it, either adding a minus sign, or 180 degrees, depending on where it is. Since it's in the 4 quadrant, simply add a minus sign

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