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Precalculus - Vectors
Terms in this set (20)
A quantity with both magnitude and direction.
One of two parts of a vector. In vector v = < a, b >, a and b are components, or coordinates, of vector v. Expressing a vector in terms of its terminal points <x,y>
The length of a vector, represented as ‖v‖. For vector v = < a, b >:
‖v‖ = √(a² + b²)
A vector u for which ‖u‖ = 1 is called a unit vector.
The vector v whose magnitude is 0 and is assigned no direction.
Standard Position Vector
A vector whose initial point is on the origin. For vector v = < a, b >, the initial point is at (0,0) and the terminal point is at (a,b).
The angle α between position vector v and the horizontal.
The multiplication of two vectors that returns a scalar as the output. Let v = a₁i + b₁j and w = a₂i + b₂j:
v * w = a₁a₂ + b₁b₂
Describes two vectors which meet at a right angle, synonymous with "perpendicular" and "normal." Two vectors v and w are orthogonal if and only if
v * w = 0
if a vector has its initial point at the origin
have the same magnitude and the same direction
the sum of two or more vectors
have the same magnitude but opposite directions
the same or opposite directions, but may not be the same magnitude
a directional measurement between 0° and 90° east or west of the north-south line
a directional measurement where the angle is measured clockwise from the north
the point of the tail of a directed line segment
Tip to tail: Translate b so the tail of b touches the tip of a
Tail to tail; translate b so the tail of b touches the tail of a. The resultant is diagonal.
head of a directed line segment
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