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.


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