Three Questions I am stuck with, uni textbook doesn't show anything for it.
#Vectors help
inner oar
autumn mossBOT
knotty frigate
Three Questions I am stuck with, uni textbook doesn't show anything for it.
for q5, part a, think about what the cross product of two vector represents, and what the dot product represents
inner oar
for q5, part a, think about what the cross product of two vector represents, and...
pff not sure
knotty frigate
part b you would use the equation in part a, and find the value for alpha which makes the equaton true
inner oar
like can you expand further
knotty frigate
do you knwo what the cross product does
inner oar
just an equation? ðŸ˜
knotty frigate
first of all does it output a scalar or a vector
inner oar
oh vector
knotty frigate
ok and a vector has magnitude and direction
so what is the significane of the direction
inner oar
not sure?
knotty frigate
the cross product of two vectors gives the vector which is perpendicular to both
so the cross product of the x and y unit vectors gives you the z vector
knotty frigate
do you know how to do the rest now
inner oar
no definitely not
knotty frigate
ok so does the dot product output a scalar or vector
inner oar
scalar
knotty frigate
ok and what does the dot product represent
what does it tell you about two vectors
knotty frigate
it tells you how much the vectors are pointing in the same direction
so perpendicular vectors are not pointing in the same direction at all, so their dot product is 0
knotty frigate
ok you should be able to do part a now
knotty frigate
if the three vectors are in a plane, and you take the cross product of two of them, how is the resulting vector related to the 3 coplanar vectors
inner oar
if the three vectors are in a plane, and you take the cross product of two of th...
its not in the same plane
its perpandicular
knotty frigate
for part a, it says the three vectors a, b, and c are coplanar
so they all lie in the same plane
inner oar
so they all lie in the same plane
nonnono
i meant
what i said
is the answer to what u said?
inner oar
if the three vectors are in a plane, and you take the cross product of two of th...
this
knotty frigate
oh yea youre right
ok so you know the cross product is perpendicular to the 3
so what happens when you take the dot product
inner oar
how much the vectors are pointing in the same direction
knotty frigate
ok and how much are they pointing in the same direction
if one is perpendicular to the other
inner oar
one is perpandicular?
inner oar
so dot product is 0?
knotty frigate
yea
a plane is defined by a perpendicular vector
because all vectors in the plane are perpendicular to a vecto pointing in one direction
and so the dot product of any vector in the plane with the perpendicular vector is 0