Find the cross products u xv and vxu for the the vectors u = 2i -j- 2k and v = i +3j - 3k.uxV=i++k (Simplify your answers.)

(.) Given vectors are, (.) Corss product of two vectors and is given by, &…

Answered: Find the cross products u xv and vxu…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Find the cross products u xv and vxu for the the vectors u = 2i -j- 2k and v = i +3j - 3k.
uxV=
i+
+
k (Simplify your answers.)

Expert Solution

Step 1: We define cross product of two vectors.

(.) Given vectors are,

$u equals 2 i minus j minus 2 k space space & space space v equals i plus 3 j minus 3 k$

(.) Corss product of two vectors $u equals u subscript 1 i plus u subscript 2 j plus u subscript 3 k$ and $v equals v subscript 1 i plus v subscript 2 j plus v subscript 3 k$ is given by,

$u cross times v space equals space open vertical bar table row i j k row cell u subscript 1 end cell cell u subscript 2 end cell cell u subscript 3 end cell row cell v subscript 1 end cell cell v subscript 2 end cell cell v subscript 3 end cell end table close vertical bar$

& $v cross times u space equals space open vertical bar table row i j k row cell v subscript 1 end cell cell v subscript 2 end cell cell v subscript 3 end cell row cell u subscript 1 end cell cell u subscript 2 end cell cell u subscript 3 end cell end table close vertical bar$