Use the given pair of vectors, u = 5i + 3j and w = 0i + 4j. Draw a picture of a vector u and vector w for which proju(w) = < 0, 0 >.

Question

Use the given pair of vectors, u = 5i + 3j and w = 0i + 4j.

Draw a picture of a vector u and vector w for which proj_u(w) = < 0, 0 >.

Answer 1

u = <5i,3j>

magnitude = sqr(25+9) = sqr31

direction = arccos(5/sqr31)=about 26.1 degrees

w = <0i, 4j>

magnitude = 4

direction = 90 degrees

projection of u on w =proj_u(w)= dot product of u and w divided by |w|= (5(0)+3(4))/4= 12/4=3= magnitude, direction 90 degrees, vector = <0i,3j>

for the magnitude to = 0, the dot product would = 0

such as u=<5i,3j> w=<0i,0j>

then projection of u on w = w=<0i,0j>