Suppose `veca` and `vecb` are vectors such that `veca` x `vecb`=(3,1,4). What is the cross product of twice of a with twice of b?

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faiz3507 | High School Teacher | (Level 2) Adjunct Educator

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notes: from the property of vectors we have (l veca x m vecb) = lm(veca x vecb),

as l veca x m vecb = | la |. | lb |. sin(la,mb). n

without loss of generality ,we may assume that a,b are non-collinear vectors.such that sin(teta) is not equal to 0 and that l,m are non-zero real numbers,

let n be a unit vector perpendicular to both veca and vacb

given (a x b) = (3,1,4)

 twice of veca = 2veca

twice of vecb = 2vecb

cross product after the change = (2a x 2b) = 4(a x b) 

plug in (a x b) = (3,1,4) 

thus we get (2a x 2b) = 4(a x b) = 4(3,1,4)

which can further be written as 4(3i+ 1j +4k) = 12i+4j+16k

thus the final answer is 12i+4j+16k