Matrici + vectors Flashcards
How do we find whether two lines are perpendicular
dot product = 0
Dot product
Dot is ez for 3x1 - just multiply x by x
for 2x2etc you do AlongxAcross + AlongXAcross
Cross product
in formula book usualy can end in (7x+2a)i - (2x+3a)j + (6a)K
find vector equation of plane ax by cz=k
can make any values you want, remember:
a must comply with n . r = k
two vectors must be perpendicular to normal!
How to find normal to a plane
Cross product of two existing vectors within the plane
Cartesian equation of a plane
n . a (normal x point on plane) = c
nx+ny+nz = c
angle between line/plane and plane
where A = line and n for the other plane
where n = normal for plane
cos(o) = (n . A-B)/{n}{A-B}
where {n} = {xyz} = sqrt(x^2 + y^2 + z^2)
how to find if matrix is singular/non
find detA = 0
A^-1
= 1/detA x (matrix flip negate)
how to find where planes meet
Mr = ijk (where ijk = solutions to each individual plane)
M= cross product of all planes in matrix form (ijk/a1b1c2/a2b2c2)
how to find equation of plane given three points A,B,C
r=A+n(B-A) + m(C-A)
how to find plane given point A and line r=B+kC
r = A + nC + m(B-A)
how to find where plane (xyz) = A and line (qpr) + K (efg) meet if at all
(q+Ke)x + (p+Kf)y + (r+Kg)z = A
how to find whether line lies in plane
when finding whether they meet, if lambda can be anything (is cancelled) then they lie within the plane
how to put vector equation of line (mn) + A(pq) into cartesian
q(y-n) = p(x-m)
how to find mutual perpendiclar to two lines
cross product of their vector
angle between two parralel lines
line1= A+D
line2 = B+D
((A-B) . D) / {A-B}{D}
