(a) Make a table that shows all possible cross products of the vectors i, j, and k . (b) Give a geometric interpretation of u × v . (c) Give a geometric interpretation of u ⋅ v × w . (d) Write an equation of the plane that passes through the origin and is perpendicular to the line x = t , y = 2 t , z = − t .
(a) Make a table that shows all possible cross products of the vectors i, j, and k . (b) Give a geometric interpretation of u × v . (c) Give a geometric interpretation of u ⋅ v × w . (d) Write an equation of the plane that passes through the origin and is perpendicular to the line x = t , y = 2 t , z = − t .
(a) Make a table that shows all possible cross products of the vectors
i, j, and k
.
(b) Give a geometric interpretation of
u
×
v
.
(c) Give a geometric interpretation of
u
⋅
v
×
w
.
(d) Write an equation of the plane that passes through the origin and is perpendicular to the line
x
=
t
,
y
=
2
t
,
z
=
−
t
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Precalculus: Mathematics for Calculus - 6th Edition
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