Question

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:

Answer #1

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-->.

Let u = (−3, 2, 1, 0), v = (4, 7, −3, 2), w = (5, −2, 8, 1).
Find the vector x that satisfies 2u − ||v||v = 3(w − 2x).

Given are V : 2x1 + 2x2 −x3 = 5
and W : x1 −x3 = 0.
1. Calculate the angle between V and W
2. Determine, independent of each other, the equation of a
paramater representation of the surface perpendicular on V and W
through point (1,2,2)

Let u=〈5,-1,6〉, v=〈0,1,2〉, and w=〈1,3,4〉. Find
(a)u×(v×w)
(b)(u×v)×w
(c)(u×v)×(v×w)
d)(v×w)×(u×v).

5.
Perform the following operations on the vectors u=(-4, 0, 2),
v=(-1, -5, -4), and w=(0, 3, 4)
u*w=
(u*v)u=
((w*w)u)*u=
u*v+v*w=

4. Given x: -3 / 0 / 3 P(X =x): .5 / .2 / .3 Find the variance
given that the expected value is - .6
A. 4.1 B. 2.85 C. 8.142 D. 2.02 E. 6.84
5. A probability distribution has a mean of 10 and standard
deviation of 1.5. Use Chevbychev’s Inequality to estimate the
probability that an outcome will be between 7 and 13.
A. 4 B. 2 C. 5 D. 4

Given the set S = {(u,v): 0<= u<=4 and 0<= v<=3} and
the transformation T(u, v) = (x(u, v), y(u, v)) where x(u, v) = 4u
+ 5v and y(u, v) = 2u -3v,
graph the image R of S under the transformation T in the
xy-plan
and find the area of region R

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
angle θ’ between u and...

1. Convert a 0.1 M NaCl to a % (w/v). 2. Convert 5% (w/v)
sucrose to a Molarity (M). 3. Which solution was more concentrated,
the 0.1 M NaCl or 5% (w/v) sucrose? 4. How could you make a dilute
solution (ex. 0.5% (w/v) sucrose) more concentrated (without adding
more sucrose)?

5. a) Suppose that the area of the parallelogram spanned by the
vectors ~u and ~v is 10. What is the area of the parallogram
spanned by the vectors 2~u + 3~v and −3~u + 4~v ?
(b) Given (~u × ~v) · ~w = 10. What is ((~u + ~v) × (~v + ~w)) ·
( ~w + ~u)? [4]
6. Find an equation of the plane that is perpendicular to the
plane x + 2y + 4 =...

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