Question

Determine whether the given vectors parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, give the acute angle between them, to the nearest degree.

a) u = 〈7, −2, 3〉

v = 〈−1, −4, 5〉

b.) u = 〈−3, 4, −6〉

v = 〈-12 , 16,- 24〉

Answer #1

Determine whether the given vectors are orthogonal, parallel, or
neither.
a = -i + 3j + 4k and b = 5i + 3j -
k
Please show all work and do not use cursive. Thank you for your
help!

1. Determine whether the lines are parallel, perpendicular or
neither. (x-1)/2 = (y+2)/5 = (z-3)/4 and (x-2)/4 = (y-1)/3 =
(z-2)/6
2. A) Find the line intersection of vector planes given by the
equations -2x+3y-z+4=0 and 3x-2y+z=-2
B) Given U = <2, -3, 4> and V= <-1, 3, -2> Find a. U
. V b. U x V

1. Compute the angle between the vectors u = [2, -1, 1] and and
v = [1, -2 , -1]
2. Given that : 1. u=[1, -3] and v=[6, 2], are u and v
orthogonal?
3. if u=[1, -3] and v=[k2, k] are orthogonal vectors.
What is the
value(s) of k?
4. Find the distance between u=[root 3, 2, -2] and v=[0, 3,
-3]
5. Normalize the vector u=[root 2, -1, -3].
6. Given that: v1 = [1, - C/7]...

1. Solve all three:
a. Determine whether the plane 2x + y + 3z – 6 = 0 passes
through the points (3,6,-2) and (-1,5,-1)
b. Find the equation of the plane that passes through the points
(2,2,1) and (-1,1,-1) and is perpendicular to the plane 2x - 3y + z
= 3.
c. Determine whether the planes are parallel, orthogonal, or
neither. If they are neither parallel nor orthogonal, find the
angle of intersection:
3x + y - 4z...

please answer all of them
a. Suppose u and v are non-zero, parallel vectors. Which of the
following could not possibly be true?
a)
u • v = |u | |v|
b)
u + v = 0
c)
u × v = |u|2
d)
|u| + |v| = 2|u|
b. Given points A(3, -4, 2) and B(-12, 16, 12), point P, lying
between A and B such that AP= 3/5AB would have coordinates
a)
P(-27/5, 36/5, 42/5)
b)
P(-6, 8,...

For the vectors Bold u equalsleft angle 3 comma 1 right angle
and Bold v equalsleft angle negative 1 comma negative 4 right
angle, express Bold u as the sum Bold u equalsBold pplusBold n,
where Bold p is parallel to Bold v and Bold n is orthogonal to Bold
v.

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

6.(a) Determine whether the lines ?1and ?2 are parallel, skew,
or intersecting. If they intersect, find the point of intersection.
[6 points] ?1: ? = 5 − 12 ?, ? = 3 + 9?, ? = 1 − 3? ?2: ? = 3 + 8?,
? = −6?, ? = 7 + 2?
(b) Find the distance between the given parallel planes. [10
points] 2? − 4? + 6? = 0, 3? − 6? + 9? = 1

Let u and v be vectors in 3-space with angle θ between them, 0 ≤
θ ≤ π. Which of the following is the only correct statement?
(a) u × v is parallel to v, and |u × v| = |u||v| cos θ.
(b) u × v is perpendicular to u, and |u × v| = |u||v| cos θ.
(c) u × v is parallel to v, and |u × v| = |u||v|sin θ.
(d) u × v is perpendicular...

Do the vectors v1 = 1 2 3 ,
v2 = √ 3 √ 3 √ 3 ,
v3 √ 3 √ 5 √ 7 ,
v4 = 1 0 0 form a basis for R 3 ? Why or why not?
(b) Let V ⊂ R 4 be the subspace spanned by the vectors a1 and
a2, where a1 = ...

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