vectors

[bross]

i have a problem that says... show that the vector(a) is perpendicular to (a-b) cross product with (a+b)

 

[Ishuda]

i have a problem that says... show that the vector(a) is perpendicular to (a-b) cross product with (a+b)

Start with things you (should) know including
x X y = - (y X x) = (-y) X x = y X (-x)
x X (y X z) = x X y + x X z
x X x = 0
a \(\displaystyle \bullet\) (a X b) = 0
and finally
a \(\displaystyle \bullet\) b = 0 if and only if a and b are orthogonal [perpendicular].

So, start playing around. If you get lost, show us your work and maybe we can help.

 

[HallsofIvy]

Or: let \(\displaystyle a= (a_1, a_2, a_3)\) and let \(\displaystyle b= (b_1, b_2, b_3)\). What is \(\displaystyle a\times b\)? What is the dot product of that with a?