Question

Can someone suggest different methods available to work out the problem given below? Pls help
Let vectora=-4i+3j-alpha k, vector b=2i+alpha j+k and vector c=5i-j+alpha k, where alpha is a real number. Show that thr vector c is not in the space spanned by vectors a and b.

Answer 1

Do you mean to say that you have to prove that vector c is not coplanar with a and b?

Answer 2

ya

Answer 3

Solve the system of equations:
-4a+3b=5
3a+alpha b=1
-alpha a+b=alpha
where a and b are coefficients to the vectors a and b.
You'll find that there is no solution with real numbers therefore c in not in the span of a and b.

Answer 4

I too did in this way. But want to know if there are other methods.

Answer 5

The box product of the vectors is not 0 if they are non coplanar.
I don't think merely solving the equations and showing they don't intersect is quite enough... Anyway do you know box product?

Answer 6

Do you mean the determinant?