Matthew Amicarelli El-Chaar course NYC-05-W13

Matthew Amicarelli El-Chaar course NYC-05-W13
NYC-Assignment-2 is due 02/04/2013 at 10:00pm EST.
The syllabus, grading policy and other information for the course can be found on Omnivox.
See online WeBWork assignment for instructions.
1. (4 pts) Suppose u = 5i + 4 j − 3k, v = −5i − 3 j + 5k and
w = 3i + 4 j + 2k.
Compute the following values:
||u|| + ||v|| =
||−7u|| + 7||v|| =
||3u − 4v + w|| =
1
||w||
w =
1
||w|| w
=
2. (4 pts) Find unit vectors that satisfy the given conditions:
(1) The unit vector in the same direction as 〈5,−5〉 is
.
(2) The unit vector oppositely directed to 4i + j + 5k is
.
(3) The unit vector that has the same direction as the vector
from the point A = (−5,5) to the point B = (−6,1) is
.
3. (3 pts) Find vectors that satisfy the given conditions:
(1) The vector in the opposite direction to u = 〈1,−2〉 and
of half its length is .
(2) The vector of length 7 and in the same direction as
v = 〈−1,−1,4〉 is .
4. (3 pts) Suppose u = 〈3,3〉 and v = 〈15,−3〉 are two vectors
that form the sides of a parallelogram. Then the lengths
of the two diagonals of the parallelogram are and
.
5. (3 pts) Suppose u = 〈−3,3,−3〉 and v = 〈−2,1,2〉. Decompose
the vector u into a sum of orthogonal vectors, one of
which is parallel to v.
(1) The vector parallel to v is .
(2) The vector orthogonal to v is .
6. (3 pts) Find two vectors v1 and v2 whose sum is 〈2,4〉,
where v1 is parallel to 〈1,−1〉 while v2 is perpendicular to
〈1,−1〉.
v1 = and
v2 = .
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7. (3 pts) Suppose u = 〈0,−5,4〉 and v = 〈−3,−1,0〉.
Compute the following vector norms:
||u + v|| =
||u − v|| =
||v − u|| =
||4u|| =
1 − 2v =
||7u − 3v|| =
8. (2 pts)
Find a ·b if a = 6, b = 10, and the angle between a and
b is π 3 radians.
a ·b =
9. (2 pts)
What is the angle in radians between the vectors a = [-10, -9,
10] andb = [-2, 9, 0]?
Angle: (radians)
10. (3 pts) Suppose u = 〈−2,1,2〉, v = 〈0,−4,2〉 and w =
〈−5,−2,0〉. Then:
u · v =
u · w =
v · w =
v · v =
u · (v + w) =
11. (4 pts) In each part, find the two unit vectors in R 2 that
satisfy the given conditions.
(1) The two unit vectors parallel to the line y = 2x − 3 are
and .
(2) The two unit vectors parallel to the line 3y − 4x = 1 are
and .
(3) The two unit vectors perpendicular to the line y = 5−4x
are
and .
12. (3 pts) Let A = (−5,3,−4), B = (2,5,2), and P =
(k,k,k). The vector from A to B is perpendicular to the vector
from A to P when
k = .
13. (1 pt)
Let a = [-10, -10, 0] and b = [7, -9, 9] be vectors. Find the
projection ofb onto a and its norm.
Projection Vector:
,
,
Norm of the Projection:

Generated by the WeBWorK system c○WeBWorK Team, Department of Mathematics, University of Rochester
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