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An object moving in the direction 120 degrees (as measured counterclockwise to the positive x axis) encounters a net force whose direction is 270 degrees.

• Sketch the force and its component along the line of motion, as well as its component perpendicular to the line of motion.
• Suppose you are facing in the direction of motion. Do you perceive the component of the force along the line of motion to be forward or backward? It this component in the direction of motion or opposite to the direction of motion?

Your sketch should show the direction vector at 120 degrees, directed from the origin into the second quadrant at 120 degrees relative to the positive y axis.

The force vector will be along the negative y axis.

From the direction vector to the force vector is a counterclockwise rotation of 120 degrees. 

If you are facing in the direction of motion, which is at the 120 degree angle, you would have to turn 150 degrees in order to face in the direction of the force.

If you were facing in the direction opposite to the motion, you would have to turn 30 degrees in order to face in the direction of the force.

So the force vector is closer to the direction opposite that of the motion than to the direction of motion.  If facing forward you would perceive the component of the force along the line of motion to be opposite the direction of the motion.

• Will the object speed up, slow down or maintain a constant speed?

The force is closer to the 'backward' direction than to the 'forward' direction so the object will slow down.

This is the same as saying that the force component along the line of motion is in the direction opposite the motion. 

A net force component in the direction opposite motion will cause the object to slow down.

• If you are facing in the direction of motion, then the line perpendicular to the direction of motion will run to your right and to your left. Is the component of the force perpendicular to the line of motion directed to the right or to the left?

If you are facing in the direction of motion at 120 deg, then to get to the 270 deg direction you would have to turn 150 deg to your left, or 210 deg to your right.  If you rotate slowly to the left you will reach the 150 deg position before you reach the 'backward' direction.  So during this rotation you are always facing somewhat to the left of your original direction. 

Thus the force vector has a component to the left, not to the right. 

• As a result the object will veer to the left.

• Will the object veer to the right, to the left or maintain straight-line motion?

The force vector has a component to the left, not to the right. 

As a result the object will veer to the left.

The component in the direction of motion is obtained by projecting the force vector onto the direction of motion, just as you would project any vector onto the direction of one of the coordinate axes. The component perpendicular to the direction of motion is obtained by projecting the vector onto a direction perpendicular to that of the motion.

• Which is greater in magnitude, the component of the force along the line of motion or the component perpendicular to the line of motion?

The two vectors are at 270 deg - 120 deg = 150 degrees. So the force vector is only 30 deg from the direction parallel to motion, which means it is 60 deg from the perpendicular direction. The component in the parallel direction is therefore greater than the component in the perpendicular direction.