Question

find any vectors which are orthogonal to the vector
<2,5,-3>

Answer #1

Any vector (x,y,z) which are orthogonal to the vector <2,5,-3>, their dot product is 0.

Thus, we get:

2x + 5y - 3z = 0

So,

.

Thus, **Any vector (x,y,z) which are orthogonal to the
vector <2,5,-3> is given by:**

**where x and y can take any value.**

For example, putting y = 1, y = 1:

the vector

i.e.,

< - 1, 1, 1> is orthogonal to the vector <2,5,-3>

because the dot product:

(-1) X 2 + 1 X 5 + 1 X (-3)

= - 2 + 5 - 3 = 0

Find any two vectors which are orthogonal to the bector
<2,5,-3>

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

What does it mean if a set of basis vectors is complete?
a. The only vector that is orthogonal to every basis vector is
the 0 vector
b. The inner product of any two basis vectors is 0
I was thinking it was B but how would it be justified

Let A be a 2x2 matrix
6 -3
-4 2
first, find all vectors V so the distance between AV and the
unit basis vector e_1 is minimized, call this set of all vectors
L.
Second, find the unique vector V0 in L such that V0 is
orthogonal to the kernel of A.
Question: What is the x-coordinate of the vector V0 equal to.
?/?
(the answer is a fraction which the sum of numerator and
denominator is 71)

Show complete solution.
1. Find two unit vectors that are parallel to the ?? −plane and
are orthogonal to the vector ? = 3? − ? + 3?.

Find two unit vectors orthogonal to both given vectors.
i + j + k,
3i + k
< _ , _ , _ > (smaller i-value)
< _ , _ , _ > (larger i-value)

Find a unit vector orthogonal to <1,3,-1> and
<2,0,3>

Find two unit vectors orthogonal to ?=〈−4,4,5〉a=〈−4,4,5〉 and
?=〈4,0,−4〉b=〈4,0,−4〉
Enter your answer so that the first vector has a positive first
coordinate

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

Prove that the orthogonal projection on the span of vectors
that are not orthogonal can be reduced to solving normal
equations. Please give an example whatever you like.

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