# 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.

https://brainmass.com/math/linear-algebra/vector-cross-products-vector-equations-154299

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Problem #1: Computer these vector quantiies

(1) , where

, ,

Thus the answer is

(2)

Problem #2: Find the characteristic equations and corresponding eigenvalues and ...

#### Solution Summary

Vector Cross-Products and Vector Equations are investigated.