Question

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 to u, and |u × v| = |u||v|sin θ.

Answer #1

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,...

Let u, v, and w be vectors in Rn. Determine which of the
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3, ?then |u?·?v| ? 5. (iii) The expression (v?·?w)u is both
meaningful and defined. (A) (ii) and (iii) only (B) (ii) only (C)
none of them (D) all of them (E) (i) only (F) (i) and...

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>

Find the angle θ (in radians and degrees) between the
lines. (Let 0 ≤ θ < π/2 and 0 ≤ θ
< 90°. Round your answers to three decimal places.)
0.02x
−
0.05y
=
−0.23
0.01x
+
0.04y
=
0.52

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(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
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d-->.

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i: Prove: U ∩V is a subspace of W.
ii: Consider the statement: “U ∪ V is a subspace of W...

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Prove that for any vector z in V whatsoever, the vectors u, v, w
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1. V is a subspace of inner-product space R3,
generated by vector
u =[2 2 1]T and v
=[ 3 2 2]T.
(a) Find its orthogonal complement space V┴ ;
(b) Find the dimension of space W = V+ V┴;
(c) Find the angle θ between u and
v and also the angle β between u
and normalized x with respect to its 2-norm.
(d) Considering v’ =
av, a is a scaler, show the
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In
3 dimensions, draw vectors u, v, w, and x such that u+v+w=x. The
vectors u and x share an initium. You may pick the size of your
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Find the angle between vector x and vector u.

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