Orthogonal unit vectors in ℝ 3 Consider the vectors I = 〈 1 / 2 , 1 / 2 , 1 / 2 〉 , J = 〈 − 1 / 2 , 1 / 2 , 0 〉 , and K = 〈 1 / 2 , 1 / 2 , − 1 / 2 〉 . a. Sketch I , J , and K and show that they are unit vectors. b. Show that I , J , and K are pairwise orthogonal. c. Express the vector 〈1, 0, 0〉 in terms of I , J , and K .
Orthogonal unit vectors in ℝ 3 Consider the vectors I = 〈 1 / 2 , 1 / 2 , 1 / 2 〉 , J = 〈 − 1 / 2 , 1 / 2 , 0 〉 , and K = 〈 1 / 2 , 1 / 2 , − 1 / 2 〉 . a. Sketch I , J , and K and show that they are unit vectors. b. Show that I , J , and K are pairwise orthogonal. c. Express the vector 〈1, 0, 0〉 in terms of I , J , and K .
Solution Summary: The author illustrates how to sketch the vectors I, J, and K using an online graphing calculator.
Orthogonal unit vectors in
ℝ
3
Consider the vectors
I
=
〈
1
/
2
,
1
/
2
,
1
/
2
〉
,
J
=
〈
−
1
/
2
,
1
/
2
,
0
〉
, and
K
=
〈
1
/
2
,
1
/
2
,
−
1
/
2
〉
.
a. Sketch I, J, and K and show that they are unit vectors.
b. Show that I, J, and K are pairwise orthogonal.
c. Express the vector 〈1, 0, 0〉 in terms of I, J, and K.
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.
The graph of f(x) is given in the figure below. draw tangent lines to the graph at x=-3,x=-2,x=1,and x=4. estimate f'(-3),f'(-2),f'(1),and f'(4). Round your answers to one decimal place.
Consider the functions f(x)=4x-1 and g(x)=sq root of -x+7. Determine
1. f o g(x)
2. Give the domain of f o g(x)
3. g o f (x)
4. Give the domain of g o f(x)
Chapter 13 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
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