1. 2. A boat travels on a heading of 335° at a constant speed of 28 km/h relative to the water. If the current is 18 km/h with a heading of 60°, what is the velocity of the ship and its bearing? Find the equation of the following lines in the required form: a. b. C. d. through the points P(1, -3,2) and Q(9,2,0) [vector equation] with direction vector d = (5,3,-4) and z-intercept 7 [symmetric equations] perpendicular to (x, y, z) = (1, -2, 0)+r(1,-1, 1) through P(1, 3, 5) [parametric equations] through T(2,-5) and perpendicular to the line 3x-6y=5 [scalar equation]

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Chapter1: Functions And Models
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Vectors
1.
2.
3.
A boat travels on a heading of 335° at a constant speed of 28 km/h relative to the water. If
the current is 18 km/h with a heading of 60°, what is the velocity of the ship and its
bearing?
Find the equation of the following lines in the required form:
a.
b.
C.
d.
through the points P(1,-3,2) and Q(9,2,0) [vector equation]
with direction vector d = (5,3,-4) and z-intercept 7 [symmetric equations]
perpendicular to (x, y, z) = (1, -2, 0)+r(1,-1, 1) through P(1, 3, 5) [parametric
equations]
through T(2,-5) and perpendicular to the line 3x-6y=5 [scalar equation]
Skew lines are lines that are not parallel, yet do not intersect, as shown in the diagram
below.
H
Show that the lines
(x, y, z)=(2, 1, 0)+ s(1, 1,-1) and
x=3+2t; y = 3t; z=-1-t
are skew.
Transcribed Image Text:Vectors 1. 2. 3. A boat travels on a heading of 335° at a constant speed of 28 km/h relative to the water. If the current is 18 km/h with a heading of 60°, what is the velocity of the ship and its bearing? Find the equation of the following lines in the required form: a. b. C. d. through the points P(1,-3,2) and Q(9,2,0) [vector equation] with direction vector d = (5,3,-4) and z-intercept 7 [symmetric equations] perpendicular to (x, y, z) = (1, -2, 0)+r(1,-1, 1) through P(1, 3, 5) [parametric equations] through T(2,-5) and perpendicular to the line 3x-6y=5 [scalar equation] Skew lines are lines that are not parallel, yet do not intersect, as shown in the diagram below. H Show that the lines (x, y, z)=(2, 1, 0)+ s(1, 1,-1) and x=3+2t; y = 3t; z=-1-t are skew.
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