# Minimum Distance Between Vector And Its Projection

This post categorized under Vector and posted on February 1st, 2020.

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Im struggling to get to an easy and simple algebraic solution for this question I actually thought about optimization with the Cauchy-Schwarz Inequality but it just got dirty and probably wrong. Also let Q (x 1 y 1) be any point on this line and n the vector (a b) starting at point Q. The vector n is perpendicular to the line and the distance d from point P to the line is equal to the graphicgth of the orthogonal projection of on n. The graphicgth of this projection is given by The graphicgth of the vector x minus v or the distance between x and some arbitrary member of our subgraphice is always going to be greater than or equal to the graphicgth of a which is just the distance between x and the projection of x onto our subgraphice. So there you have it. Weve shown and the original graph kind of hinted at it that the projection of x onto v is the closest vector in our

Scalar and vector projections are determined using the dot product and the minimum distance between a point and a line is determined as an application of the orthogonal projection. I did this question by projecting vector x onto subgraphice S (i did the projection of x onto w1 w2 w3) However when i asked professor about this question he told that in order to find the minimum distance between a vector and subgraphice we need to produce an orthogonal basis for S and only then do the projection of vector x onto orthogonal basis. Finding the distance between a point and a plane means to find the shortest distance between the point and the plane. This is made difficult due to the fact that we dont know the point on the

Use the parametric equations to find a vector that gives direction numbers and a coordinate point. Find a vector between the two coordinate points. Then take the cross product of the two vectors Dot Product - Distance between Point and a Line Beakal Tiliksew Andres Gonzalez and Mahindra Jain contributed The distance between a point and a line is defined as the shortest distance between a fixed point and any point on the line. Check out httpwww.engineer4get.com for more get engineering tutorials and math lessons Linear Algebra Tutorial Find the distance from a point to a lin (Note that we can also find this by subtracting vectors the orthogonal projection orth a b b - proj a b. Make sure this makes sense) Points and Lines. Now suppose we want to find the distance between a point and a line (top diagram in figure 2 below).