Question #a42a8

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Answer 1 · 2017-03-18T05:31:36

Let

$veca=hati-2hatj+hatk$
and
$vecb=3hati+hatj-2hatk$

The cross product of these two vectors ( $veca and vecb$ ) is a vector $vecc$ perpendicular to both as shown in the figure below

google image

So
$vecc =veca xxvecb=[(hati,hatj,hatk),(hati,-2hatj,hatk),(3hati,hatj,-2hatk)]$

$=((-2)*(-2)-1*1)hati+(1*3-1*(-2))hatj+(1*1-3*(-2))hatk$

$=3hati+5hatj+7hatk$

So unit vector of $vecc=vecc/abs(vecc)$

$=(3hati+5hatj+7hatk)/sqrt(3^2+5^2+7^2)$

$=(3hati+5hatj+7hatk)/sqrt83color(red)(->"option (2)")$