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q   =   (2.2, 3.6)T
r   =   (-4.8, -2.2)T
s   =   q + r

Answer:

| q |   =  Sqrt( 2.2*2.2 + 3.6*3.6 )   =  Sqrt( 4.84 + 12.96 )   =  Sqrt 17.8   =   4.219
| r |   =  Sqrt( -4.8* -4.8 + -2.2 * -2.2 )   =  Sqrt( 23.04 + 4.84 )   =  Sqrt 27.88   =   5.280
| s |   =  Sqrt( -2.6 * -2.6 + 1.4*1.4 )   =  Sqrt( 6.76 + 1.96 )   =  Sqrt 8.72   =   2.953

As expected, | s | is less than | q | + | r |.

Length of 3D Vectors

Three dimensional vectors have length. The formula is about the same. The length of a vector represented by a three-component matrix is:

| (x, y, z)T |  =  Sqrt( x2 + y2 + z2)

For example:

| (1, 2, 3)T |   =  Sqrt( 12 + 22 + 32 )

  =  Sqrt( 1 + 4 + 9 )  =  Sqrt14   =   3.742

QUESTION 8:

What is the length of   (2, -4, 4)T

What is the length of   (-1, -2, 3)T