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from manimlib.imports import *
class Projections(GraphScene):
CONFIG = {
"x_min": -6,
"x_max": 6,
"y_min": -4,
"y_max": 4,
"graph_origin" : ORIGIN ,
}
def construct(self):
self.setup_axes(animate=True)
XTD = self.x_axis_width/(self.x_max-self.x_min)
YTD = self.y_axis_height/(self.y_max-self.y_min)
arrow_a = Arrow(start = ORIGIN, end = 4*XTD*RIGHT)
arrow_a.scale(1.2)
arrow_a.set_color(DARK_BLUE)
arrow_b = Arrow(start = ORIGIN, end = 2*YTD*UP+2*XTD*RIGHT)
arrow_b.scale(1.3)
arrow_b.set_color(DARK_BLUE)
self.play(ShowCreation(arrow_a), ShowCreation(arrow_b))
text = TextMobject(r"Consider 2 linearly independent vectors $a$ and $b$")
text.set_color(DARK_BLUE)
text.scale(0.6)
text.move_to(3*YTD*UP+5*XTD*LEFT)
text_a = TextMobject("a")
text_a.move_to(0.4*YTD*DOWN+3*XTD*RIGHT)
text_a.set_color(DARK_BLUE)
text_b = TextMobject("b")
text_b.move_to(1.5*YTD*UP+RIGHT*XTD)
text_b.set_color(DARK_BLUE)
self.play(Write(text),Write(text_a), Write(text_b))
self.wait()
arrow_b_copy = Arrow(start = ORIGIN, end = 2*YTD*UP+2*XTD*RIGHT)
arrow_b_copy.scale(1.25)
arrow_p = Arrow(start = ORIGIN, end = 2*XTD*RIGHT)
arrow_p.scale(1.5)
arrow_p.set_color(GOLD_E)
text_p = TextMobject("p")
text_p.move_to(0.25*DOWN+RIGHT)
text_p.set_color(GOLD_E)
self.play(FadeOut(text), Transform(arrow_b_copy,arrow_p), FadeOut(text_a), FadeOut(text_b))
text = TextMobject(r"$p$ is the projection of $b$ on $a$")
text.set_color(GOLD_E)
text.move_to(3*UP+4*LEFT)
text.scale(0.8)
self.play(Write(text),Write(text_p))
self.wait()
self.play(FadeIn(text_a), FadeIn(text_b))
arrow_o = Arrow(start = 2*XTD*RIGHT, end = 2*YTD*UP+2*XTD*RIGHT)
arrow_o.scale(1.5)
arrow_o.set_color(GREEN_E)
text_o = TextMobject("b-p")
text_o.move_to(UP*YTD+2.7*XTD*RIGHT)
text_o.set_color(GREEN_E)
self.play(ShowCreation(arrow_o))
self.play(FadeOut(text),Write(text_o))
text = TextMobject(r"Observe, ($b-p$) is orthogonal to $a$")
text.set_color(GREEN_E)
text.move_to(2*DOWN+4*LEFT)
text.scale(0.8)
self.play(Write(text))
self.wait(2)
self.play(FadeOut(self.axes), FadeOut(arrow_a), FadeOut(arrow_b), FadeOut(arrow_b_copy), FadeOut(arrow_o), FadeOut(text_a), FadeOut(text_b), FadeOut(text_o), FadeOut(text_p), FadeOut(text))
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