Question

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>

Answer #1

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

Find two vectors v1 and v2 whose sum is 〈1,3〉, where v1 is
parallel to 〈1,2〉 while v2 is perpendicular to 〈1,2〉.
v1 =
and
v2 =

Find two non-parallel vectors v1 and v2 in R2 such that
||v1||2=||v2||2=1 and whose angle with [3,4] is 42 degrees. *Note:
[3,4] is a 2 by 1 matrix with 3 on the top and 4 on the bottom.

2. Two vectors, ~v1 and ~v2. ~v1 has a length of 12 and is
oriented at an angle θ1 = 30o relative to the positive x−axis. ~v2
has a length of 6 and is oriented at an angle θ2 = 0o relative to
the positive x−axis (it is aligned with the positive x−axis)
a. What are the magnitude and direction (angle) of the sum of
the two vectors ( 1+2 ~v = ~v1 + ~v2)?
b. What are the magnitude...

Find two vectors v¯¯¯1 and v¯¯¯2 whose sum is 〈5,1〉, where v¯¯¯1
is parallel to 〈5,−1〉 while v¯¯¯2 is perpendicular to 〈5,−1〉 .
v¯¯¯1 = and v¯¯¯2 =

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) 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)

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...

Two vectors are given by; A ⃗=(2i ̂+3j ̂+4k ̂)units B ⃗=(4i ̂+6j
̂+8k ̂)units If it is known that ;
a.A ⃗+B ⃗+2C ⃗=0, Find C ⃗.
b. Find (A ⃗+2C ⃗).2B ⃗.
c.Find (A ⃗×B ⃗)
d.Find (A ⃗+B ⃗+2C ⃗)×(2A ⃗+B ⃗)

Find the angle θ between the vectors (,) and (-2,-4).

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