In: Math
for u=<2,1,-3> and v=<1,0,2>,
a) find the angle between u and v
b) use the formula proj_a b=((a•b)/|b|^2)b to find vector projection of v onto u
c) sketch vectors u, v, and the projection found with only using arrows
d) find the area of the parallelogram determined by u and v
Taking dot product of the vectors
where is angle between u and v.
2) the vector projection of v onto u is given by
By properties of dot product
based on previous question
3) the projection of vector v onto u is given by
4) Area of parallelogram = magnitude of cross product
AREA OF PARALLELOGRAM