Question

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for u=<2,1,-3> and v=<1,0,2>, a) find the angle between u and v b) use the formula...

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

Solutions

Expert Solution

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

milcah answered 1 year ago

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