Posted by Anonymous on Sunday, March 30, 2008 at 10:57am.
Given two noncollinear vectors a and b, show that a, axb, and (axb)xa are mutually perpendicular.
Also
Express the unit vectors i, j, and k as ordered triplets and show that
i x j = k
what are ordered triplets?
Using components show that
u x v = v x u for any vectors u and v.

Math  drwls, Sunday, March 30, 2008 at 11:26am
A cross product is always perpendicular to BOTH vectors, unless it the cross product is zero, which happens only for collinear vectors.
Therefore (a x b) is perpendicular to a.
My statement also proves that (axb)x a is perpendicular to both a and a x b
The "proof" they want you to do involves actually computing the cross product of a x b where a = i and b = j. You will end up proving that the cross product is k. Use these "ordered triplet" designations:
i = (1 0 0)
j = (0 1 0)
k = (0 0 1)
i x j = value of the determinant
i j k
1 0 0
0 1 0 = 0i + 0j + k

Math  drwls, Sunday, March 30, 2008 at 11:35am
Your last question <<Using components show that u x v = v x u for any vectors u and v.>>
can be done similarly using arbitrary ordered triplet designations for u and v,
u = ai + bj + ck
v = di + ej + fk
where a, b, c, d, e and f are arbitrary constants and then using the determinant formula to compute the cross products. u x v and v x u
u x v =
i j k
a b c
d e f
= (bf  ce)i + (cd  af)j + (ae  bd)k
Now compare that to v x u =
i j k
d e f
a b c = (ec  bf)i, etc
Answer This Question
Related Questions
 Mamthematics  Vectors  a) If vector u and vector v are noncollinear vectors ...
 perpendicular vectors  Find two unit vectors each of which is perpendicular to ...
 Vectors  the vector a5b and ab are perpendiculat. If vector a and b are unit ...
 Math please help  For the first question I really need all help I can get. ...
 maths  Given that vector c and vector d are non zero vectors such that vector c...
 Math  Let a, b, and c be unit vectors, such that a+b+c=0. Show that the angle ...
 Math  Write XY as the sum of unit vectors for X(8,2,9)and Y(12,1,10). First...
 physics (cross product vectors)  Two vectors are lying in the xz plane: A=2.00i...
 Vectors and Geometry  if A=i+j, B=2i3j+k and C=4j3k find (i) (AxB)xC & Ax(BxC...
 math  given that vectors(p+2q) and (5p4q) are orthogonal,if vectors p and q ...
More Related Questions