Question

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).

Answer #1

For parts ( a ) − ( c
) , let u = 〈 2 , 4 , − 1 〉 and v = 〈 4 , − 2 , 1 〉 .
( a ) Find a unit
vector which is orthogonal to both u and v .
( b ) Find the vector
projection of u onto v .
( c ) Find the scalar
projection of u onto v .
For parts ( a ) − (...

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

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.

Let u = [-2,1,3,1] and let v = [1,4,0,1]. a. Determine the
projector P1 that projects onto the subspace S1 spanned by the
vector u. What isthe rank of P1? b. Determine the projector that
projects onto the orthogonal complement of S1. c. Determine the
projector P2 that projects onto the subspace S2 spanned y the
vectors {u,v}. What is the rank of P2? d. Determine an orthogonal
projector that projects onto the orthogonal complement of S2. e.
Verify that...

Find the angle theta between vectors u=(5,6) and v=(-8,7).
Find a unit vector orthogonal to v.

1. Let ⃗u = −2[4,0,1]+[−1,3,−2] and ⃗v = 3[4,0,1]+5[−1,3,−2].
Let w⃗ = 3⃗u−⃗v. Express w⃗ as a linear combination of the vectors
[4, 0, 1] and [−1, 3, −2].
2. Let ⃗u and ⃗v be two vectors in Rn. Suppose that ||⃗u|| = 3,
||⃗u − ⃗v|| = 5, and that⃗u.⃗v = 1. What is ||⃗v||?.
3. Let ⃗u and ⃗v be two vectors in Rn. Suppose that ||⃗u|| = 5
and that ||⃗v|| = 2. Show that ||⃗u −...

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

Given vector ? = 2? + 3?, ? = −5? + ? + ?. Find the
followings.
a) The projection of u onto v
b) A vector that is orthogonal to both u and v

Let u=[6,2 ], v=[3,3 ], and b=[4,1 ]. Find
(x⋅u+y⋅v-b)×2 u, where x,y are scalars.

Let vector u= 5i+3j+8k and vector v= i-j+2k
Find the component of v parallel to u and the component of v
perpendicular to u
find a unit vector perpendicular to both u and v

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 34 minutes ago

asked 35 minutes ago

asked 44 minutes ago

asked 44 minutes ago

asked 50 minutes ago

asked 50 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago