If A makes the ________ with the +x- axis, then its x- and y- components are Acosθ and Asinθ respectively (where A is the magnitude of A)
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same direction
The product is a vector with twice the magnitude and, since the scalar is positive, the ________ is A.
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55 miles
________ per hour is a scalar (like mass, work, energy power, temperature change)
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Displacement
________ (which is the difference between the final and initial positions) is the prototypical example of a vector: A (________)= 4 miles (magnitude) to the north (direction)
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Direction of kA
________= the same as A if k is positive or the opposite of A if k is negative.
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dot product
The ________ or scalar product is a scalar that results from multiplying the magnitude of one vector with the magnitude of the component of another vector that is parallel to the first:
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Vectors
________ obey the commutative law for addition.
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Scalar multiplication
________: multiply each component by the scalar.
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B
The vector sum A + ________ means the vector A followed by ________, while the vector sum ________ + A means the vector ________ followed by A.
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angle θ
The direction of any vector, A, can be specified by the ________, it makes with the positive x- axis such than tan (θ)= A** ᵧ /** Aₓ.
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If A makes the angle θ with the +x-axis, then its x
and y-components are Acosθ and Asinθ respectively (where A is the magnitude of A)
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Vector addition is carried out with the "tip-to-tail" method
place the tail of one vector at the tip of the other vector, then connect the exposed tail to the exposed tip
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Vector subtraction is carried out with the "tip-to-tail" method, but the negative second vector is added A
B = A + (-B)
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Vectors can be expressed in terms of components using the unit basis vectors to indicate direction
i indicates the +x-direction, j indicated the +y-direction, and k indicates the +z-direction
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Vector addition
add respective components
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Vector subtraction
subtract the respective components
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Scalar multiplication
multiply each component by the scalar
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The magnitude of any vector, A, can be computed by applying the Pythagorean Theorem to the scalar components of the sector, Aᵧ and Aₓ
A = √(Aₓ)^2 + (Aᵧ)^2
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The cross product is a vector that has magnitude that results from multiplying the magnitude of one vector by the magnitude of the component of another vector thats perpendicular to the first
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