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Ede4ka [16]
3 years ago
11

Find a unit vector that is orthogonal to both u and v. u = −8, −6, 4 v = 10, −18, −2

Mathematics
1 answer:
Delvig [45]3 years ago
5 0
A vector w orthogonal to u and v can be obtained by the cross product of u and v, namely u x v.  Subsequently, u x  v may be reduced to a unit vector.

u<-8,-6,4>
v<10,-18,-2>

w=u x v 
=
  i      j   k
 -8   -6  4
10 -18 -2
=<12+72, 40-16, 144+60>
=<84, 24, 204>
=12 < 7,2,17>

Check that w is orthogonal to u and v
w.u = 12<7,2,17><-8,-6,4> = 12(-56-12,68)=0
w.v = 12<7,2,17><10,-18,-2> = 12(70-36-34)=0
Therefore w is orthogonal to both u and v.

Unit vector of w
\frac{}{\sqrt{7^2+2^2+17^2}}=\frac{1}{3\sqrt{38}}
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