How do you find two unit vectors orthogonal to A=(1, 3, 0) B =(2, 0, 5) first vector must have positive first coordinate?

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Answer 1 · 2016-07-01T12:36:15

$+-(1/sqrt 286)(15, -5, -6)$

Let C(a, b, c) be a vector orthogonal to A(1, 3, 0) and B(2, 0, 5).

Then, $A.C=0=B.C$ .

So, a+3b=0 and 2a+5b=0. Eliminating b and c,

C becomes $(a, -a/3, -2a/5)=a(1, -1/3, -2/5)$

So, the unit vectors in opposite directions that are orthogonal to A

and B are

$+-(1/sqrt(1^2+(1/3)^2+(2/5)^2))(1, -1/3, -2/5)$

$= +-(1/sqrt 286)(15, -5, -6)$