Homework SourseIf u 3i 2j and v 5i 3j find a the unit vector in the directi
If u= 3i +2j and v= -5i +3j, find
a) the unit vector in the direction of u
b) the dot product of the vectors
c) the vector projection of v onto u
d) the vector projection of u onto v
a) the unit vector in the direction of u
b) the dot product of the vectors
c) the vector projection of v onto u
d) the vector projection of u onto v
Solution
a)unit vector = (3i+2j)/sqrt(13)
b)dot product = u.v = (5*-3) + (2*3) = -15+6 = -9
c) angle b/w u and v is cosθ = (u.v)/(mod u).(mod v) = -0.954
θ = 162.5
projection of v on u = (mod v)*cosθ*u = -16.68i - 11.12k
d) projection of u on v = (mod u)*cosθ*v = 17.2i - 10.32k
