Question

2. Given the vectors ? = (−2,1,2) and ? = (1, − 3, 1), find: a) The dot product b) The cross product c) The angle between the vectors

Answer #1

1. Given the point P(5, 4, −2) and the point Q(−1, 2, 7) and
R(0, 3, 0) answer the following questions • What is the distance
between P and Q? • Determine the vectors P Q~ and P R~ ? • Find the
dot product between P Q~ and P R~ . • What is the angle between P
Q~ and P R~ ? • What is the projP R~ (P R~ )? • What is P Q~

Find the angle between the vectors < 1, 2, –2 > and < 4
,0, –3 >.

1) Given two vectors A? = 4.20 i^+ 7.20
j^ and B? = 5.80 i^? 2.60 j^ ,
find the scalar product of the two vectors
A? and B? .
2) Find the angle between these two vectors.

1) Consider two vectors A=[20, 4, -6] and B=[8, -2, 6].
a) compute their dot product A.B
b) Compute the angle between the two vectors.
c)Find length and sign of component of A over B (mean Comp A
over B)and draw its diagram.
d) Compute Vector projection of B over A (means Proj B over A)
and draw corresponding diagram.
e) Compute Orthogonal projection of A onto B.

Two vectors given below, A and B, are located in a standard 3-D
cartesian coordinate system: A = 5i + 2j - 4k B = 2i + 5j + 5k a.
Find the magnitude of the sum of A and B. b. Find the dot product
of A and B. What does this result tell you about A and B? c. Find a
vector C, with non-zero magnitude, that is perpendicular to both A
and B.

Find an inner product such that the vectors ( −1, 2 )T and ( 1,
2 )T form an orthonormal basis of R2
2
4.1.11. Prove that every orthonormal basis of R2 under the
standard dot product has the form u1 =
cos θ
sin θ
and u2 = ±
− sin θ
cos θ
for some 0 ≤ θ < 2π and some choice of ± sign.
.

a) Given two vectors A⃗ =4.00i^+7.20j^ and B⃗ =5.30i^−2.10j^,
find the scalar product of the two vectors A⃗ and B⃗
Part B) Find the angle between these two vectors. Express your
answer in degrees.

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) 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>

What is the effect on the dot product of two vectors, if the
angle between the two vectors is fixed, but one of the vectors
doubles in length? or triples in length?
two explainations please

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