How to 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 · 2018-05-22T18:43:32

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

For ease of writing, suppose that, #barw=(a,b,c)#.

Given that, #barwxx(2,0,-2)=(4,0,4)#, we have,

#|(i,j,k),(a,b,c),(2,0,-2)|=4i+oj+4k#.

#:. -2bi+(2a+2c)j-2bk=4i+0j+4k#.

#:. -2b=4 and 2a+2c=0#.

#:. b=-2 and c=-a.................(star)#.

It is also known that, #||barw||=2#.

#:. sqrt(a^2+b^2+c^2)=2, i.e., a^2+b^2+c^2=4#.

#"Then, by "(star)," we have, "a^2+(-2)^2+(-a)^2=4#.

#:. 2a^2+4=4 rArr a=0 rArr c=-a=0#.

Thus, altogether, #a=0, b=-2, c=0#.

Hence, #barw=(a,b,c)=(0,-2,0)#