Calculus 2 Test 1
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Dot Product vs Cross Product
- Dot = Scalar
- Cross = Vector
a1b1 + a2b2 + a3b3
Can dot product be used in 2 dimensions?
Dot product relates to
the angle between two vectors
Two vectors are orthogonal if the angle between them is
Two vectors are orthogonal when a*b is equal to
Two vectors are parallel if theta equals
zero or pi
Projections can be
scalar or vector
Projection of vector b onto vector a
- Assigned length of the Projection
What is an application of dot product?
Can cross product be used in 2 dimensions?
No... it MUST be 3d
Av X Bv
- There is a formula, but memorize the process
- Use determinants
Why is the cross product important?
Av X Bv => 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!!
What would you like to do?
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