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Math 141 · Lesson 21

Vector Projection

Drag two vectors to get the projection of v̄ onto ū, the closest multiple of ū to v̄. The worked solution, the residual and the R code update as the vectors move.

Lesson 21: Vector Projection

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About this tool

Show numbers works out the projection scalar

x=v‾⋅u‾u‾⋅u‾,x = \frac{\overline{v} \cdot \overline{u}}{\overline{u} \cdot \overline{u}},

the projection xu‾x\overline{u} and the residual r‾=v‾−xu‾\overline{r} = \overline{v} - x\overline{u}. The panel also checks that r‾⋅u‾=0\overline{r} \cdot \overline{u} = 0.

Under More:

  • Closest multiple. Candidate x slides a candidate xx. The plot of ∥v‾−xu‾∥\lVert \overline{v} - x\overline{u} \rVert against xx is lowest at the projection scalar.
  • Sketch. The hand-drawing recipe, one step at a time with the arrow buttons. All steps shows every step at once.

Keys: press V or U to pick a tip. Press an arrow key to move it one grid step. Hold Shift with an arrow key to move it five steps. Press Esc to let go. In Sketch, after Esc, the left and right arrow keys step through the recipe.