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Vectors have magnitude and direction. The magnitude is always a positive number.
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 null vector has no magnitude, a negative vector does have a magnitude but it is in the direction opposite to that of the reference vector.
No, the value can't be negative because magnitude of a vector is just how long it is regardless of its direction. :-)
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.
Vectors have magnitude and direction. The magnitude is always a positive number.
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°.
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
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 null vector has no magnitude, a negative vector does have a magnitude but it is in the direction opposite to that of the reference vector.
No, the value can't be negative because magnitude of a vector is just how long it is regardless of its direction. :-)
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)
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.
It is a vector that has the opposite direction to the reference positive direction. (A vector is one point in space relative to another.) Negative vector is the opposite direction
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.
Yes, "velocity" is a vector so it not only has magnitude but also direction. By convention, an object moving from left-to-right or upward is moving in a positive direction while an object moving right-to-left or downward is moving in a negative direction. "Speed" is a related term but it is a scalar. As such, it has only magnitude. A speed cannot be negative.