Vectors Flashcards
What does the dot product of two vectors give
A scalar
Why is the dot product useful
Allows the angle between two vectors to be found
How is the dot product used to know if two vectors are perpendicular
The dot product will =0
What does the cross product go two vectors give
Another vector
What direction is the vector of the cross product
It is normal to the plane of the two original vectors
How to find area of a triangle between a, b and the origin
Magnitude of the cross product divided by two
What is the magnitude of the cross product
Are of the parallelogram formed by a and b
When are two vectors parallel
If one is a scalar multiple of the other
What is the vector equation of a straight line
r=a+t(b-a)=a+tc
Where a is a point on the line and c is the tangent vector
r=(x,y,z)
Vector equation of a plane
N•(r-r0)
r=position vector of any point (x,y,z) on the plane
r0=position vector of a known point (x0,y0,z0) on the plane
n=normal vector(a,b,c)
how to calculate what component of a is in the direction of b
a*b/|b|=|a|cos x
Equation of a plane through point (x0,y0,z0) with normal vector (n1,n2,n3)
N1(x-x0) +n2(y-y0) +n3(z-z0)=0
Shortest distance between two 3D lines
d= |(a-b)•(d1xd2)|/|d1xd2|
