Question

Convert a position expressed in one of the vector notations to the others

From

• Magnitude and Angle Form

• Cartesian Component Form

• Magnitude, Direction, Sense Form

Answer 1

Suppose we have a force (of magnitude = 5) denoted in 2 dimensions x and y as

Magnitude = 5 and it makes an angle of 53.13 degrees with the +ve x axis as shown

Magnitude and Angle Form

So the angle theta is given by tan(theta) = 4/3 = 1.3333 and so theta = 53.13 degrees

So the Force of 5 can be written as magnitude 5, angle 53.13 degrees

Cartesian Coordinate Form

So in cartesian coordinates form, the point P which represents the force of 5 can be written as

OP = 3ˆi + 4ˆj

Magnitude , Direction and Sense Form

The force of 5 can be written as a magnitude of 5, ''up and to the left" making an angle of 53.13 degrees with the +ve x axis.