Answer :

Given, and


We need to find a vector perpendicular to and such that.


Recall a vector that is perpendicular to two vectors and is



Here, we have (a1, a2, a3) = (1, 4, 2) and (b1, b2, b3) = (3, –2, 7)






So, is a vector parallel to.


Let for some scalar λ.



We have.




λ[(2)(32) + (–1)( –1) + (4)(–14)] = 15


λ(64 + 1 – 56) = 15


9λ = 15



So, we have.


Thus,


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