How do you solve the equation 𝑤̅×<2,0,−2>=<4,0,4> where 𝑤̅=<𝑤1,𝑤2,𝑤3> is nonzero with a magnitude of 2?

1 Answer
Jul 27, 2018

barw=(0,-2,0)¯¯¯w=(0,2,0).

Explanation:

Given, barwxx(2,0,-2)=(4,0,4)," where, "barw=(w_1,w_2,w_3).¯¯¯w×(2,0,2)=(4,0,4), where, ¯¯¯w=(w1,w2,w3).

Now, barwxx(2,0,-2)=(4,0,4)¯¯¯w×(2,0,2)=(4,0,4).

:. |(i,j,k),(w_1,w_2,w_3),(2,0,-2)|=4i+0j+4k.

;. -2w_2i-(-2w_1-2w_3)j+(-2w_2)k=4i+0j+4k.

:. -2w_2=4, 2w_1+2w_3=0 and -2w_2=4,

i.e., w_2-2, w_1=-w_3, and, w_2=-2.....(ast_1).

Finally, utilising ||barw||=2, we have,

w_1^2+w_2^2+w_3^2=4...........................(ast_2).

From (ast_1) and (ast_2), (-w_3)^2+(-2)^2+w_3^2=4,

or, 2w_3^2=0 rArr w_3=0 rArr w_1=0......[because (ast_1)].

Thus, barw=(w_1,w_2,w_3)=(0,-2,0), as desired!