X - component = 7.3 cos(250) = -2.497 meters (rounded)
Y - component = 7.3 sin(250) = -6.86 meters (rounded)
It's pointing down and slightly to the left ... like south-southwest.
Another 20 degrees and it would be pointing straight down.
Vectors have magnitude and direction. The magnitude is always a positive number.
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Yes, acceleration can be positive and negative because acceleration is a vector. It has both direction and magnitude. The direction is what makes it positive or negative. Negative acceleration is usually called deceleration.
A vector has both magnitude and direction. The magnitude is always positive, by convention, but this is not cast in stone. So you can have in your case a positive magnitude with a direction 257.31 degrees, which is the same as a positive magnitude 77.31 degrees in quadrant III, but the first way is more conventional. One could also say a negative magnitude at 77.31 degrees, in which case the negative sign implies a 180 degree reversal. So there are many choices, and you seem to have a good handle on this.
No. Cos theta (Cos θ) is a trigonometric function. A vector is any physical quantity which has both magnitude and direction. For example, Displacement. Displacement has a magnitude like 240m or 0 or 13 m, etc. It also depends on the direction. If an object moves along the positive direction of x-axis, then the displacement will have a positive sign and if it moves along the negative direction of x-axis, then displacement will be negative. Thus, it has both direction and magnitude and so is a vector. Cos theta is a trigonometric function, strictly speaking.
Vectors have magnitude and direction. The magnitude is always a positive number.
speed is a scalar quantity with magnitude only but no direction; velocity is a vector with both magnitude (speed) AND direction, which could be positive or negative
The resultant magnitude is 60.659 N and its vectorial angle is 356.6124 degrees.
Magnitude is the absolute value which is always positive.--Edit: Magnitude is a scalar quantity thus regardless of the direction of the vector (which determines is positivity or negativity) the magnitude would be positive.Example: you take two steps forwards; the magnitude is two steps, regardless of it being forward or backwards (positive or negative)
Torque has the direction perpendicular to the plane of the twist. The Right-Hand Rule says positive torque is counterclockwise(ccw).
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A vector has both magnitude and direction. The magnitude is always positive, by convention, but this is not cast in stone. So you can have in your case a positive magnitude with a direction 257.31 degrees, which is the same as a positive magnitude 77.31 degrees in quadrant III, but the first way is more conventional. One could also say a negative magnitude at 77.31 degrees, in which case the negative sign implies a 180 degree reversal. So there are many choices, and you seem to have a good handle on this.
scalar quantity has only magnitude whereas vector quantity has magnitude as well as direction
Yes, acceleration can be positive and negative because acceleration is a vector. It has both direction and magnitude. The direction is what makes it positive or negative. Negative acceleration is usually called deceleration.
A positive scalar multiplied by a vector, will only change the vector's magnitude, not the direction. A negative scalar multiplied by the vector will reverse the direction by 180°.
If you define the positive direction as pointing down, then the falling object has positive acceleration.Its magnitude is 9.8 m/s2.
Take the component of the acceleration along the direction the object is moving. If this component is positive (the acceleration vector, or the relevant component, points in the same direction as the movement), then the object is speeding up.