Let and Find a vector which is perpendicular to both and and
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,