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?

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Answer 1 · 2018-07-27T06:01:14

# barw=(0,-2,0)#.

Given, #barwxx(2,0,-2)=(4,0,4)," where, "barw=(w_1,w_2,w_3).#

Now, #barwxx(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!