Chapter 11 Vectors Flashcards
what qualities do vectors have?
magnitude and direction
how can you represent a vector?
using a directed line segment
what happens if two vectors are equal? (PQ = RS)
the line segments will be equal in length and parallel
what happens if a vector is equal to the negative of another vector? (AB = -BA)
the line segment 1 (eg AB) is equal in length, parallel and in the opposite direction to line segment 2 (BA)
what is the triangle law for vector addition?
AB + BC = AC
what is subtracting a vector equivalent to?
adding a negative vector
eg: a - b = a + (-b)
what happens if you add the vectors PQ and QP?
you get 0
what can vectors parallel to vector a be written as?
lambda a where lambda is non-zero scalar
how do you multiply a column vector by a scalar?
lambda(p/q) = lambda p/lambda q
how do you add two column vectors?
p/q + r/s = p + r/q + s
how would you write the column vector a/b as a unit vector?
ai + bj
how do you find the magnitude of a vector?
magnitude of vector ai + bj = √a^2 + b^2
how do you calculate AB with position vectors?
AB = OB - OA where OA and OB are the position vectors of a and b
if point P divides the line segment AB in the ration lambda : mu then what is OP?
OP = OA + lambda / (lambda + mu) x (OB - OA)
if a and b are 2 non-parallel vectors and pa+qb=ra+sb then what does p and q equal?
p = r and q = s
