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Answer 1 · 2017-04-02T17:05:46

A. Parallel

Given: #vecv=3hati+2hatj#, #vecw=6hati+4hatj#

Compute the Dot Product :

#vecv*vecw = 3(6)+(2)(4)#

#vecv*vecw = 26#

The Dot Product is not 0, therefore, the vectors are not Orthogonal

Compute the magnitudes of both vectors:

#|vecv| = sqrt(3^2+2^2)#

#|vecv| = sqrt(9+4)#

#|vecv| = sqrt(13)#

#|vecw| = sqrt(6^2+4^2)#

#|vecw| = sqrt(36+16)#

#|vecw| = sqrt(52)#

Use an alternative definition of the Dot Product:

#vecv*vecw = |vecv||vecw|cos(theta)#

where #theta# is the angle between the two vectors.

Substitute in the known values:

#26 = sqrt(13)sqrt52cos(theta)#

#26 = sqrt(676)cos(theta)#

#26 = 26cos(theta)#

#cos(theta) = 1#

#theta = 0#

This indicates that the two vectors are parallel.