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Gravity
Terms in this set (20)
What makes a vector perpendicular/orthogonal to another vector?
if the dot product is = 0
What makes a vector parallel to another vector?
if the normal vector is a scalar multiple of another
What equation do we use when finding the equation of a plane that passes thru point (2,4,1) with n=<3,-1,4>?
n=<a,b,c> (2,4,1) = (Xo,Yo,Zo)
ax+by+cz=d
d=aXo+bYo+cZo
How do we find the intersection point of two lines
r(t)=<1,0,0>+t1<-2,7,0>
s(t)=<0,1,1>+t2<-5,0,7>
Also to find a point that lies on the line?
1) break into parametric equations
2) use 2 equations to solve for t1 and t2
3) use 3rd equation to verify values of t1 and t2
4) input t1 and t2 into parametric equations to find the intersection point
1) set t=whatever and insert into parametric equation
Checking if a point (-1,4,3) is on the line r(t)=<5,0,2>+t<3,1,-4>
plug in <-1,4,3> to the parametric equations, if all t's are equal then YES it is on the line
finding coordinates of a point that lies on a line
make -∞<t<∞, (ex. t=2) plug into parametric equations
area of a triangle spanned by two vectors v and w
A= 1/2 ||vxw||
area of a parralelogram/parralelpiped spanned by 2 vectors v and w
A = 2 ||vxw||
finding the point of intersection between 3x+2y-z=12 and -4x+3y-1z=-14
plug in parametric equations from one into another ex
3(-4+2t)+2(3-t)-z(-1+3t)=12
then solve for t
plug t into parametric equations
find parametric equations for a line that is parallel to <2,0,-3> and passes through (7,-4,1)
Which one is used as <x,y,z> which is <xo,yo,zo>
parallel to = xo,yo,zo>
passes through = <x,y,z>
finding the interception with x axis for 3x+2y-z=12
3x+2(0)-(0)=12
3x=12
x=4 (4,0,0)
finding the interception with y axis for 3x+2y-z=12
3(0)+2y+(0)=12
2y=12
y=6 (0,6,0)
finding the interception with z axis for 3x+2y-z=12
3(0)+2(0)-z=12
z=-12
(0,0,-12)
A= <1,2,3>
B= <0,2,4>
C= <5,1,2>
finding the area of this triangle
A= 1/2 ||AB x AC||
Find the normal vector
A= <1,2,3>
B= <0,2,4>
C= <5,1,2>
||AB x AC||
for what values of m will <1,2m,3> and <2,1,4m> be orthogonal?
set dot product = 0, solve for m
proj U on V
(U•V)/(V•V) * V
Proj V on U
(V•U)/(U•U) * U
Comp U on V
U • V
Θ = ?
cos^-1(A•B)/(||A||B||)
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