b. An airliner flies northwest at a constant altitude at 550 mi/hr relative to the air in a southerly crosswind w = (0, 40). Find the velocity of the airliner relative to the ground.
b. An airliner flies northwest at a constant altitude at 550 mi/hr relative to the air in a southerly crosswind w = (0, 40). Find the velocity of the airliner relative to the ground.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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#17 part b
Transcribed Image Text:4. u+2v
5. 2v -u
6-15. Working with vectors Let u = (2, 4,-5), v = (-6, 10, 2), and
w = (4,-8, 8).
6. Compute u – 3v.
7. Compute |u+v[.
8. Find the unit vector with the same direction as u.
9. Write the vector w as a product of its magnitude and a unit vector in
the direction of w.
10. Find a vector in the direction of w that is 10 times as long as w.
11. Find a vector in the direction of w with a length of 10.
12. Compute u · v
13. Compute u × v
14. For what value of a is the vector v orthogonal to y= (a, 1, –3)?
15. For what value of a is the vector w parallel to y =
(a, 6, –6)?
16. Scalar multiples Find scalars a, b, and c such that
(2, 2, 2) = a(1, 1, 0) + b(0, 1, 1) + c(1, 0, 1).
17. Velocity vectors Assume the positive x-axis points east and the
positive y-axis points north.
a. An airliner flies northwest at a constant altitude at 550 mi/hr in
calm air. Find a and b such that its velocity may be expressed in
the form v = ai + bj.
b. An airliner flies northwest at a constant altitude at 550 mi/hr
relative to the air in a southerly crosswind w =
(0, 40). Find
the velocity of the airliner relative to the ground.
18. Position vectors Let PQ extend from P(2, 0, 6) to Q(2, –8, 5).
a. Find the position vector equal to PQ.
b. Find the midpoint M of the line segment PQ. Thend the
magnitude of PM.
C. Find a vector of length 8 with direction opposite to that of PQ.
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s and balls Use set notation to describe the following sets.
Expert Solution
Step 1
Given the velocity of the crosswind in the south direction is .
The objective is to find the velocity of the airline relative to the ground.
Velocity of the moving object relative to the ground equal to velocity of the moving object in steady air plus velocity of the air.
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