Card Set Information
A Quantity that can be expressed by a single number Ex. mass, speed, volume, distance, temperature, work.
A quantity that has direction and magnitude. Ex. velocity, force, displacement, Torque
Vectors that that have the same magnitude, opposite direction. AB=-BA
Vectors that have the same magnitude and the same direction. AB=AB
Vectors that have different magnitudes, and same or opposite direction. AB=kAB
Direction of a Vector
The angle a vector makes when it is placed tail-to-tail with another vector.
A vector with a magnitude of 1. It is equal to a vector divided by its magnitude.
A vector that has a magnitude of zero and direction undefined. It looks like a point.
The sum of 2 vectors (w=u+v)
The ability to switch the positions of 2 vectors in vector addition and the dot product.
The ability to group vectors together when doing vector operations.
The ability to distribute vectors when doing scalar multiplication.
The rule that the magnitude of the resultant vector cannot be greater than the sum of the magnitudes of the 2 other vectors.
lu+vl<_lul + lvl
State of Equilibrium
When the resultant of vectors is the zero vector (3 vectors make a triangle)
The capacity to do work or cause physical change. F=ma
The force that attracts a body towards the centre of the earth or any other physical body that has mass. G=mg (g=9.8m/s2)
Shows the position of vectors acting on an object (directly from the question)
Shows the vector operation that determines the resultant (after manipulating the vectors)
The force parallel to the ramp which causes the object to slide down. (Fp+Fn=G)
The force perpendicular to the force parallel that pushed towards the ramp.
The velocity of the wind pushing in a certain direction. Vw+Vg=Va
The velocity of the plane when it is near the ground (without wind)
The velocity of the plane in the air. The resultant of the wind velocity and the ground velocity.
Directed line segment.
Directed line segment represented with components. v=(a,b)
One Dimensional Vectors
Vectors on a line.
R Two Space
A vector with 2 dimensions (x and y)
R Three Space
A vector with 3 dimensions (x,y, and z)
A vector with its tail in the origin.
A unit vector parallel to the x axis.
A unit vector parallel to y axis.
A unit vector parallel to the z axis.
Unit Vector notation
OP=ai^+bj^+ck^ - A vector represented as the vector sum of scalar multiples of its unit vectors.
Ordered pair/Ordered triple notation
OP=(a,b,c) - Vector represented with its components.
The formulas to find the angles between the vector v and the x,y, and z axis (in R three space)
Direction of a vector in an R Two Space
The angle between the vector and the positive x axis.
The coordinates of the endpoint of a position vector.
The Dot product
The dot product between two vectors is defined by the product of their magnitudes and the cosine angle between the two vectors. It is a scalar value.
The Cross product
The cross product (x) between the vectors a and b is a vector represented by axb with the following properties:
1. axb is perpendicular to a and b
2. The magnitude of axb is lallblsin@
3. a, b, and axb form a right handed system
The vector projection (a onto b) is the "shadow" a imposes on b. It is formed by dropping a perpendicular from the tip of a onto b.
A rectangular prism tilted on an angle.
The turning effect of a force causing an angular effect. (Vector)
When a force acts on an object and displaces it. (Scalar)
Vectors are coplanar when they are in the same plane.
2 lines in an R three space that are not parallel but they never intersect.
A type of matrix when the leading entries go down and two the right. Also all the entries below the leading entries are zero and all all zero entries are at the bottom.
The process of transforming an augmented matrix into Echelon form.
A matrix that forms an equation (dotted line represents and = sign)
Row reduced Echelon form
A type of matrix when:
1. The leading entries go down and to the right
2. The leading entries are all ones
3. There are only zeros above and below the leading entries
4. All all zero rows are at the bottom
The process of transforming an augmented matrix into row reduced Echelon form.