In each part, use the result in Exercise 45 to prove the vector identity. a a × b × c × d = a × b ⋅ d c − a × b ⋅ c d b a × b × c + b × c × a + c × a × b = 0
In each part, use the result in Exercise 45 to prove the vector identity. a a × b × c × d = a × b ⋅ d c − a × b ⋅ c d b a × b × c + b × c × a + c × a × b = 0
In each part, use the result in Exercise 45 to prove the vector identity.
a
a
×
b
×
c
×
d
=
a
×
b
⋅
d
c
−
a
×
b
⋅
c
d
b
a
×
b
×
c
+
b
×
c
×
a
+
c
×
a
×
b
=
0
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.
2. Determine whether the expression is defined or undefined. If it is defined, then
determine whether it is a vector or a scalar. If it is undefined, explain why.
a xỉ
a.
b.
||à × ī||
c. (ā× b) + (è ×ā)
d. (āxb).c
e. (ā·b) + č
f. (a.b) + (c. d) + 3
g. a. (b.c)
Use the accompanying figure to write each vector listed as a linear combination of u and v.
th
Vectors c, x, y, and z
-2v
Write c as a linear combination of u and v.
u+
V
(Type integers or decimals.)
Thomas' Calculus: Early Transcendentals (14th Edition)
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