) A classmate says they think of vector projections as shadows. Explain the connection between a vector and a shadow. Draw a picture if helpful.

Question

A classmate says they think of vector projections as shadows. Explain the connection between a vector and a shadow. Draw a picture if helpful.

Answer 1

picture a children's slide at noon with the sun casting a shadow on the ground

the slide is a vector with length 5 yards and direction, maybe 45 degrees

the projection onto the ground, the x axis is the length of the shadow of the slide on the ground = square root of 2 times 5 divided by 2 = 2.5sqr2 = about 2.5(1.414) = 3.5355 yds direction 0 degrees

=5cos(theta) = 5cos45 = 5(sqr2/2) = about 3.5355

the vector <3.5355, 0>