Find the plane through the origin (0,0,0) and perpendicular to the vector (v1) . So I thought to find the normal vector by the cross products of (v1) and some other vector. But I can not seem to find the other vector. Any ideas?

Question

Find the plane through the origin (0,0,0) and perpendicular to the vector (v1) <1, -2, 5> .
So I thought to find the normal vector by the cross products of (v1) and some other vector. But I can not seem to find the other vector. Any ideas?

rational · Answer

<1, -2, 5>  itself is the normal vector

rational · Answer

Can you write the equation of plane using the given point ?

anonymous · Answer

$$n _{1}(x _{1}-x _{0})+n _{2}(y _{1}-y _{0})+n _{3}(z _{1}-z _{0})=0$$
Thus: x-2y+5z=0
So they gave me the normal vector. Makes more sense. I think I was thrown off by the perpendicular part of the question for some reason. Thanks for the help rational!

rational · Answer

yw!