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Calculus 2 Test 1
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Dot Product vs Cross Product
Dot = Scalar
Cross = Vector
a
_{v}
*b
_{v}
=>
a
_{1}
b
_{1}
+ a
_{2}
b
_{2}
+ a
_{3}
b
_{3}
Can dot product be used in 2 dimensions?
Yes
Dot product relates to
the angle between two vectors
Two vectors are orthogonal if the angle between them is
pi/2
Two vectors are orthogonal when a*b is equal to
zero
Two vectors are parallel if theta equals
zero or pi
Projections can be
scalar or vector
Proj
_{a}
b
Projection of vector b onto vector a
Scalar Proj
_{a}
b
Assigned length of the Projection
(a
_{v}
*b
_{v}
)/a
_{v}

What is an application of dot product?
Work
Can cross product be used in 2 dimensions?
No... it MUST be 3d
A
_{v}
X B
_{v}
There is a formula, but memorize the process
Use determinants
Why is the cross product important?
A
_{v }
X B
_{v}
=> Perpendicular to both vectors
Right hand rule
Shows which way the cross product vector will point
How to find unit vector
Divide by vector's magnitude
How are cross products useful?
For finding area
I, J, K are related... how do we remember this?
Remember the i > j > k cycle for cross product!!
Author:
Larabeth
ID:
167574
Card Set:
Calculus 2 Test 1
Updated:
20120827 00:28:28
Tags:
Calculus Vectors
Folders:
Description:
MA126
Show Answers:
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