Posted by Wanda on Sunday, March 2, 2008 at 11:31am.
what you want here is the cross-product for the 2 vectors [4,2,-3] and [2,-3,1]
an algebraic approach is to let that vector be [a,b,c],
then [a,b,c]∙[4,2,-3] = 0
and [a,b,c]∙[2,-3,1] = 0
from the first: 4a+2b-3c=0
from second: 2a-3b+c=0
double the second and subtract it from the first:
8b-5c=0
8b=5c
b/c = 5/8
let b=5 and c=8 back in first
4a + 10 -24 = 0
a=7/2
so a possible vector is [7/2,5,8] or
[7,10,16]
You can check that the dot product with each of the original vectors is zero, it works.
but you wanted a unit vector.
The magnitude of [7,10,16] is √(7^2+10^2+16^2) = √405
so the unit vector which is perpendicular to both is [7/√405,10/√405,16/√405]
there is a nice algorithm to find the cross product between two vectors [a,b,c] and [d,e,f]
line up the numbers above each other
a b c
d e f
the cross product is
[bf-ec,-(af-dc),ae-bd]
I follow this method,
block out the first column with my finger, then take the difference in the products of the diagonals of the remaining 2by2
block out the middle column with my finger , then take the -(difference in the products of the diagonals of the remaining 2by2)
block out the last column with my finger, then take the difference in the products of the diagonals of the remaining 2by2
e.g.
4 2-3
2-3 1
cross product is
[2-9,-(4+6),-12-4]
=[-7,-10,-16] which is a multiple of [7,10,16 from above.
HEYYYYRwei
Related Questions
Math: Vectors - Find any vector w that is perpendicular to both vector "u...
math - the position vectors of the point A,B & C respect to O are a=3i-2j+4k...
maths - 1.IF Vector OA =2i + 3j – k, vectorOB = i – 2j + 3k determine ...
algebra - Find the angles between the following pairs of vectors (1)3i+2j-6k,4i-...
algebra - Find the angles between the following pairs of vectors (1)3i+2j-6k,4i-...
physics - A=2i+3j-k, b=4i=2j-2k, find the vector x parallel to A but has ...
math - Find the vector eqn which passes through (1,1,2) and is parallel to the ...
physics - Find a vector of magnitude 18 which is perpendicular to both the ...
vectors - Given the vectors v=-2i+5j and w=3i+4i, determine (do I just plug what...
Help on Vectors & Geometry - (a) Given that A= 3i - j + 2k and B=2i + 3j - k...
For Further Reading
