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Plane perpendicular to a vector

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The scalar product or dot product, allows you to tell if two vectors are orthogonal or perpendicular among other things. So if you can visualize that the vector [tex] (2, 3, 4)^{T} [/tex] must be orthogonal to every point in the plane then the plane through the origin with normal vector [tex] (2, 3, 4)^{T} [/tex] would be given by the equation [tex] 2x + 3y +4z = 0 [/tex]. 2021. 5. 21. · We know position vector of a point (x, y, z) is given by \(\text x\hat i+y\hat j+z\hat k\), where , and are unit vectors along X, Y and Z directions. Similarly, we have. Plane ABC contains the two vectors \(\vec {AB}\) and \(\vec{AC}\). So, a vector perpendicular to this plane is also perpendicular to both of these vectors. I use this in my master thesis to find one of the two vectors that span a plane (where the input is the normal vector to the plane). The other vector that spans the plane is of course the cross. Find an equation of a plane passing through the point given and perpendicular to the given vector. Point: (-2,10,2) Vector v= (-4,2,3) Submitted: 10.