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
following statements are always true. (i) If ||u|| = 4, ||v|| = 5,
and ?||u + v|| = 8, then u?·?v = 4. (ii) If ||u|| = 2 and ||v|| =
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>

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]...

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-->.

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

3. Let P = (a cos θ, b sin θ), where θ is not a multiple of π/2
be a point on the ellipse (x 2/ a2 )+ (y 2/ b 2) = 1, where a ≥ b
> 0; and let P1 = (a cos θ, a sin θ) the corresponding on the
circle x 2 /a2 + y 2/ a2 = 1. Prove that the tangent to the ellipse
at P and the tangent to the circle at...

Let U and V be subspaces of the vector space W . Recall that U ∩
V is the set of all vectors ⃗v in W that are in both of U or V ,
and that U ∪ V is the set of all vectors ⃗v in W that are in at
least one of U or V
i: Prove: U ∩V is a subspace of W.
ii: Consider the statement: “U ∪ V is a subspace of W...

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.

Let u = <3, 2, 5> and v = <-2,5,4>
Compute the angle between u and v b)
Compute proj v u

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