Traditional Culture Encyclopedia - Photography major - What is the orthogonal projection number of vector A = (5,2) in the direction of vector B = (-2, 1)? How to understand the number of orthographic projection and the difference between orthographic pro

What is the orthogonal projection number of vector A = (5,2) in the direction of vector B = (-2, 1)? How to understand the number of orthographic projection and the difference between orthographic pro

What is the orthogonal projection number of vector A = (5,2) in the direction of vector B = (-2, 1)? How to understand the number of orthographic projection and the difference between orthographic projection and projection? Hello, orthographic projection refers to the vertical line from a point to a straight line, and vertical foot is projection.

The orthogonal projection of vector A in direction B is a vector, that is, the vector from the origin to the projection point.

The projection in the vector refers to the quantity, that is, the projection of A in the direction B: | a | * cos < a, b>.

A = (5,2) and b=(-2, 1), then: |a|=sqrt(29), |b|=sqrt(5), and: a b =-8.

Therefore: cos

Therefore, the projection of a: | a | * cos (π-

=( 16/5,-8/5)

A's projection in direction B: | a | * cos < a, b> = sqrt (29) * (-8/sqrt (29 * 5)) =-8/sqrt (5) =-8 sqrt (5)/5.