Q: What are the x component and the y component of a vector a in the xy plane if its direction is 250 degrees counterclockwise from the positive direction of the x axis and its magnitude is 7.3 m?

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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.

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Vectors have magnitude and direction. The magnitude is always a positive number.

The resultant magnitude is 60.659 N and its vectorial angle is 356.6124 degrees.

Velocity includes both speed and direction, so a negative velocity indicates motion in the opposite direction. Speed, on the other hand, is a scalar quantity representing the magnitude of velocity without regard to direction, and therefore is always positive.

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 is a vector quantity represented by both magnitude and direction. The direction of torque is perpendicular to the plane formed by the force applied and the point of rotation. It follows the right-hand rule, where the direction of torque can be determined by curling your right hand around the axis of rotation in the direction of the force.

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Positive velocity refers to an object moving in the positive direction along its path. It indicates that the object is moving forward or in the direction of increasing position. Velocity is a vector quantity that includes both magnitude (speed) and 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 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.

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 180Â°.

Velocity can be negative or positive because it is a vector quantity that includes both magnitude (speed) and direction. A positive velocity indicates movement in one direction, while a negative velocity indicates movement in the opposite direction. This allows us to distinguish between forward and backward motion.

Speed in a given direction refers to velocity, which is a vector quantity that includes both the magnitude (speed) and direction of an object's motion. It describes how fast an object is moving in a specific direction.