Vector...Plx help!

a. a‧b = │a││b│cos@ = (sqrt3)(2)(1/2 sqrt3) = 3

│a + b│ = sqrt[│a + b│^2] = sqrt[│a│^2 + │b│^2 + 2a‧b]

= sqrt[(sqrt3)^2 + (2)^2 + 2(3)] = sqrt13

│a X b│ = │a││b│sin@ = (sqrt3)(2)(1/2) = sqrt3


b. By Gauss Jordan Elimination:

1 -1 0 1 0 0
1 0 -3 → 0 1 0
2 1 -2 0 0 1
2 -1 1 0 0 0

Deleting the last row, it is an identity matrix. the coefficients are uniquely determined to be all equal 0

So, the three vectors are linearly independent.

2010-05-06 20:22:48 補充：
au + bv + cw = 0
For u, v and w to be linearly independent, a, b and c are all zero