Question:
Vector Cross Products and Vector Equations
Compute these vector quantities.
1) (i+3j-k) X (4i-j+2k)
2) (-i+3j+4k) X [(2i-j-k)x(i+j-3k)]
Find the characteristic equation for the matrix below and determine its eigenvalues and the corresponding eigenvalues.
-2 4 0
1 1 0
-3 4 3
Find the equations for the indicated geometrical objects:
1) The plane containing the line (3t,-t,1-2t) and orthogonal to the plane x-4y+3z=5.
2) The line through the point (2,-1,3) and perpendicular to the plane x-4y+3z=5.