Given v = 4 , − 3 and w = 2 , − 2 , a. Find proj w v . b. Find vectors v 1 and v 2 such that v 1 , is parallel to w, v 2 is orthogonal to w, and v 1 + v 2 = v . c. Using the results from part (b) show that v 1 is parallel to w by finding a constant c such that v 1 = c w . d. Show that v 2 is orthogonal to w. e. Show that v 1 + v 2 = v .
Given v = 4 , − 3 and w = 2 , − 2 , a. Find proj w v . b. Find vectors v 1 and v 2 such that v 1 , is parallel to w, v 2 is orthogonal to w, and v 1 + v 2 = v . c. Using the results from part (b) show that v 1 is parallel to w by finding a constant c such that v 1 = c w . d. Show that v 2 is orthogonal to w. e. Show that v 1 + v 2 = v .
Solution Summary: The author calculates the vector projection v=4,-3andw =2,-2.
b. Find vectors
v
1
and
v
2
such that
v
1
, is parallel to w,
v
2
is orthogonal to w, and
v
1
+
v
2
=
v
.
c. Using the results from part (b) show that
v
1
is parallel to w by finding a constant c such that
v
1
=
c
w
.
d. Show that
v
2
is orthogonal to w.
e. Show that
v
1
+
v
2
=
v
.
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)
College Algebra with Modeling & Visualization (5th Edition)
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