Let N ^ represent the direction horizontally north, NE ^ represent northeast (halfway between north and east), and so on. Each direction specification can be thought of as a unit vector. Rank from the largest to the smallest the following dot products. Note that zero is larger than a negative number. If two quantities are equal, display that fact in your ranking. (a) N ^ • E ^ (b) N ^ • NE ^ (c) N ^ • S ^ (d) N ^ • E ^ (e) SE ^ • S
Let N ^ represent the direction horizontally north, NE ^ represent northeast (halfway between north and east), and so on. Each direction specification can be thought of as a unit vector. Rank from the largest to the smallest the following dot products. Note that zero is larger than a negative number. If two quantities are equal, display that fact in your ranking. (a) N ^ • E ^ (b) N ^ • NE ^ (c) N ^ • S ^ (d) N ^ • E ^ (e) SE ^ • S
Solution Summary: The author explains the rank of cases from largest to smallest. Write the expression for scalar product of two vectors.
Let
N
^
represent the direction horizontally north,
NE
^
represent northeast (halfway between north and east), and so on. Each direction specification can be thought of as a unit vector. Rank from the largest to the smallest the following dot products. Note that zero is larger than a negative number. If two quantities are equal, display that fact in your ranking. (a)
N
^
•
E
^
(b)
N
^
•
NE
^
(c)
N
^
•
S
^
(d)
N
^
•
E
^
(e)
SE
^
• S
For vectors ū and ū, suppose ||ü|| - 5, the angle between the vectors is 170 degrees, and the dot product
ü-i = -8. Find the magnitude of vector i . Leave at least 4 decimals place. Don't round.
Consider the vectors A = -
(a) cos
171.8
(b) sin
A . B
AB
-2î + 5ĵ - 4k and B = 5î − 7ĵ + 6k. Calculate the following quantities. (Give your answers in degrees.)
|A x B|
AB
O
46.3
Review the formula for calculating the vector product directly from components. Be careful of the signs in your calculation. Be sure to take the magnitude
of the result of the vector product. Be sure to find the angle in degrees and not radians. º
(c) Which give(s) the angle between the vectors? (Select all that apply.)
The answer to Part (a).
The answer to Part (b).
Use the definition of scalar product, a = ab cos 0, and the fact that a
.
the two vectors given by a = 3.01 +3.0
+ 3.0k and b
Number
i
Units
= axbx + ab + a₂b₂ to calculate the angle between
4.0î + 9.0ĵ + 7.0k.
=
Chapter 7 Solutions
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