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.
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.
=
Two vectors have the following magnitude, A= 10.7 m and B = 9.8 m. Their vector product is:
AxB = -4.2 mi+7.5 m k.
What is the angle (in degrees) between the vectors A and B?
Hint: Use
Note: Bold face letters represents a vector.
|AxB| = AB sin(0)
Chapter 7 Solutions
Physics for Scientists and Engineers With Modern Physics
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