Question

Consider the following.

**u** =

−6, −4, −7

, **v** =

3, 5, 2

(a) Find the projection of **u** onto
**v**.

(b) Find the vector component of **u** orthogonal to
**v**.

Answer #1

U= [2,-5,-1] V=[3,2,-3] Find the orthogonal projection of u onto
v. Then write u as the sum of two orthogonal vectors, one in
span{U} and one orthogonal to U

Let u = ⟨1,3⟩ and v = ⟨4,1⟩.
(a) Find an exact expression and a numerical approximation for
the angle between u and v. (b) Find both the projection of u onto v
and the vector component of u orthogonal to v.
(c) Sketch u, v, and the two vectors you found in part
(b).

Find the orthogonal projection of u onto the
subspace of R4 spanned by the vectors
v1, v2 and
v3.
u = (3, 4, 2, 4) ;
v1 = (3, 2, 3, 0),
v2 = (-8, 3, 6, 3),
v3 = (6, 3, -8, 3)
Let (x, y, z, w) denote the
orthogonal projection of u onto the given
subspace. Then, the components of the target orthogonal projection
are

2.
a. Given u = (9,7) and v = (2,3), find the projection of u onto
v. (ordered pair)
b. Find the area of the parllelogram that has the given vectors
u = j and v = 2j + k as adjacent sides.

12. a.) If u = (0, 2, 3) and v = (1, 3, -1), find the projection
of u onto v
b.) What type of answer is produced by the expression displayed
below. a→·(b→×c→)
c.) What type of answer is produced by the expression displayed
below. (b→−c→)×a→ d
.) What type of answer is produced by the expression displayed
below. (a→·b→)+(b→·c→)

Matrix A= -2 1 0
2 -3 4
5 -6 7
vector u= 1
2
1
a) Is the vector u in Null(A) Explain in detail why
b) Is the vectro u in Col( A) Explain in detail why

let x=u+v. y=v find dS, the a vector, and ds^2 for the u,v
coordinate system and show that it is not an orthogonal system

Find the following for the vectors u= -10+9j+√3k and v=
10i-9j-√3k.
a) v*u, |v|, and |u|.
b) the cosine of the angle between v and u.
c) the scalar component of u in the direction of v
d) the vector projvu

Consider the following:
period 1, 2, 3, 4, 5, 6, 7, 8
demand 7, 8, 9, 10, 14, 16, 13, 16
a. using a trend projection, forecast the demand for period
9
b. calculate the MAD for this forecast
Show all work! do not use excel or phstat!!!

Find the orthogonal projection of v=[−2,10,−16,−19] onto the
subspace W spanned by [-4,0,-2,1],[-4,-2,5,1],[3,-1,-3,4]

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