Vector Algebra and Coordinate Geometry Flashcards
When are two vectors equal?
If they have the same length and magnitude
What equations are definite if vectors a=b?
|a| = |b| and a is parallel to b
What equations are definite if vectors ha=kb where h and k a scalar multiples
|ha| =|hb| and a is parallel to b
or, h = k = 0 if a is not parallel to b
Midpoint of vector AB given the vectors a and b
(a+b)/2
Dot product formula
a.b = |a||b| cos θ
where θ is the angle between the two vectors
Line ratio rule given coordinates
If a = x(1)i + y(1)j and b = x(2)i + y(2)j, then
a x b = x1x2 + y1y2
Given point which divides AB by ratio γ:µ (which are non-negative real numbers) find the length connecting the origin to this point
Magnitude of a vector given its coordinates
Distance of a vector given the coordinates
If the position vectors of the vertices of a triangle are a, b, c, then what is the position vector of the centroid?
(a + b + c) / 3
First add the three vectors together to create a new column vector and multiply that by 1/3
The coordinates of a centroid given the coordinates of the triangle’s vertices
Find out if three points, P,Q and R, are collinear using vectors
Three points Q, R, and P are collinear if the sum of the lengths of any two line segments among PQ, QR, and PR is equal to the length of the third line segment:
PQ + QR = PR
or PR +RQ = PQ
or QP + PR = QR
Second method to find dot product
a · b = ax × bx + ay × by
How to find the unit vector of a vector?
Either (1/vector magnitude) x vector or:
Midpoint formula given the coordinates
Gradient of a line formula
