Question

2. Given ⃗v = 〈3,4〉 and w⃗ = 〈−3,−5〉 find

(a) comp⃗vw⃗

(b) proj⃗vw⃗

(c) The angle 0 ≤ θ ≤ π (in radians) between ⃗v and w⃗.

1. Let d^{-->} =2i−4j+k. Write⃗a=3i+2j−6k as the sum
of two vectors⃗v,w⃗, where⃗v is perpendicular

to d^{-->} and w⃗ is parallel to
d^{-->}.

Answer #1

5)
a: Letd=2i−4j+k.
Write⃗a=3i+2j−6kasthesumoftwovectors⃗v,w⃗,where⃗visperpendicular
⃗⃗ to d and w⃗ is parallel to d.
b: Find the equation of the plane through the origin and
perpendicular to x+y+z = 5 and 2x+y−2z = 7

1) Let a = 2i −4j +4k and b= 7i −6j +6k . Find a⋅b
2) Let a = 〈−4,0,1〉 and b = 〈1,2,3〉 Find a×b
3) Let a = 〈−5,1,−4〉 and b = 〈−1,0,−4〉. Find the angle between
the vector (in radians)

Find an equation of a sphere with the given radius r
and center C. (Use (x,
y, z) for the coordinates.)
r =
7; C(3, −5, 2)
Find the angle between u and
v, rounded to the nearest tenth degree.
u = j + k,
v = i +
2j − 5k
Find the angle between u and
v, rounded to the nearest tenth degree.
u = i + 4j −
8k, v =
3i − 4k
Find a vector that...

A) Find the angle between the vectors 8i-j + 4k and 4j + 2k
B) Find c so that the vectors 2i-3j + ck and 2i-j + 4k are perpendicular
C) Find the scalar projection and the vector projection of 2i +
4j-4 on 3i-3j + k

1) Find the angle θ between the vectors a=9i−j−4k and
b=2i+j−4k.
2) Find two vectors v1 and v2 whose sum is <-5,
2> where v1 is parallel to <-3 ,0> while v2 is
perpendicular to < -3,0>

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...

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 −...

1. Calculate sin (x + y) when sin (x) = 0.20 (0 < x < π/2)
and
sin (y) = 0.60 (π/2 < y< π) .
2. Find two vectors that have the same magnitude and are
perpendicular
to 3i + 5j
3. Two vectors are given by a = 3i + 2j and b = −i + 5j.
Calculate the
vector product of axb.

4. Given v= < -3, 2 > and w = < 5, - 4 >, find:
a) v + w
b) 3v – w
c) | v | =
d) The angle between v and w:

(a) In unit vector notation, what is r = a - b + c if:
a=5i+4j-6k, b = -2i + 2j+3k, & c = 4i+3j+2k?
(b) Calculate the angle between r and the positive z-axis
(c) What is the component of a along the direction of b?
(d) What is the component of a perpendicular to the direction of
b but in the plane of a and b?
I did a b and c. However, for question C I don't...

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