We use PQ to denote the vector with initial point P and ...
We use PQ to denote the vector with initial point P and terminal point Q.
A vector is a force that has both magnitude and direction.
The direction is indicated by the arrow at the terminal point.
The magnitude is the length of the segment representing the vector. || v ||
A vector that represents a pull or push of some type is a force vector.
A single force that represents the combined forces of two combined vectors is a resultant force. We use a parallelogram to determine the resultant force.
mv is a scalar multiple of the vector v. If m > 0 then it has the same direction as v.
If m < 0 then it has the opposite direction as v.
By placing a vector’s initial point at the origin, the xy-plane is used to represent the vector. The numbers a1 and a2 are the components of vector < a1, a2 >.
The direction of the vector is determined by graphing a1 and a2.
The magnitude of the vector is the length of the segment.
Magnitude of a vector: [pic]
Addition of vectors: [pic]
Subtraction of vectors: [pic]
Scalar multiple of a vector: [pic]
Special vectors [pic] are unit vectors of magnitude 1.
These vectors can be used as an alternate way of denoting vectors: [pic]
Sketch vectors a and b, then find and sketch 2a, – b, a + b, a – b, and 3a + 2b
[pic] [pic]
Find the magnitude of a and the smallest positive angle ( from the positive x-axis to the vector OP that corresponds to a.
[pic] [pic]
The vectors a and b represent two forces acting at the same point, and ( is the smallest positive angle between a and b. Approximate the magnitude of the resultant force.
a = 40 lb, b = 70 lb ( = 45( a = 30 kg, b = 50 kg, ( = 150(
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