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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.