Hexagonal sphere packing Imagine three unit spheres (radius equal to 1) with centers at O (0, 0, 0), P ( 3 , − 1 , 0 ) , and Q ( 3 , 1 , 0 ) . Now place another unit sphere symmetrically on top of these spheres with its center at R (see figure). a. Find the coordinates of R . ( Hint: The distance between the centers of any two spheres is 2.) b. Let r ij be the vector from the center of sphere I to the center of sphere J. Find r OP , r OQ , r PQ , r OR , and r PR .
Hexagonal sphere packing Imagine three unit spheres (radius equal to 1) with centers at O (0, 0, 0), P ( 3 , − 1 , 0 ) , and Q ( 3 , 1 , 0 ) . Now place another unit sphere symmetrically on top of these spheres with its center at R (see figure). a. Find the coordinates of R . ( Hint: The distance between the centers of any two spheres is 2.) b. Let r ij be the vector from the center of sphere I to the center of sphere J. Find r OP , r OQ , r PQ , r OR , and r PR .
Solution Summary: The author explains that the coordinates of R are (2sqrt3,0) and
Hexagonal sphere packing Imagine three unit spheres (radius equal to 1) with centers at O(0, 0, 0),
P
(
3
,
−
1
,
0
)
, and
Q
(
3
,
1
,
0
)
. Now place another unit sphere symmetrically on top of these spheres with its center at R (see figure).
a. Find the coordinates of R. (Hint: The distance between the centers of any two spheres is 2.)
b. Let rij be the vector from the center of sphere I to the center of sphere J. Find rOP, rOQ, rPQ,rOR, and rPR.
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.
For the following function f and real number a,
a. find the slope of the tangent line mtan
=
f' (a), and
b. find the equation of the tangent line to f at x = a.
f(x)=
2
=
a = 2
x2
a. Slope:
b. Equation of tangent line: y
Please refer below
Chapter 13 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
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