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What is the orientation of u = (-4, -2)T ?

Answer:

By plugging into the formula (and using inv tan of the MS Win calculator):

arc tan( y/x )   =   arc tan( -2/-4 )   =   arc tan( 0.5 )   =   26.565°

But from the sketch, this is in the wrong quadrent. Study the sketch and use geometry to see that the answer must be (180 + 26.565 )° = 206.565°.

Calculating both Attributes

Say that (using a particular coordinate frame) you know that a vector is represented by (x, y)T.

You can calculate the two attributes of the vector:

orientation of (x, y)T = arc tan( y/x )
|(x, y)T| = ( x2 + y2 )

In a few pages we will start with length and orientation and calculate the x and y for a particular coordinate frame.

QUESTION 6:

Sketch the vector r represented by (4, 5)T. Make an eyeball estimate of its length and direction. Then do the math to get the exact answer.