(a) Sketch vectors u and v for which u + v and u − v are orthogonal. (b) How can you use vectors to determine whether four points in 3-space lie in the same plane? (c) If forces F 1 = i and F 2 = j are applied at a point in 2-space, what force would you apply at that point to cancel the combined effect of F 1 and F 2 ? (d) Write an equation of the sphere with center 1 , − 2 , 2 that passes through the origin.
(a) Sketch vectors u and v for which u + v and u − v are orthogonal. (b) How can you use vectors to determine whether four points in 3-space lie in the same plane? (c) If forces F 1 = i and F 2 = j are applied at a point in 2-space, what force would you apply at that point to cancel the combined effect of F 1 and F 2 ? (d) Write an equation of the sphere with center 1 , − 2 , 2 that passes through the origin.
(a) Sketch vectors u and v for which
u
+
v and u
−
v
are orthogonal.
(b) How can you use vectors to determine whether four points in 3-space lie in the same plane?
(c) If forces
F
1
=
i and F
2
=
j
are applied at a point in 2-space, what force would you apply at that point to cancel the combined effect of
F
1
and F
2
?
(d) Write an equation of the sphere with center
1
,
−
2
,
2
that passes through the origin.
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.
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