Question

State True or False.

The following position vectors are collinear.

$3a-4b+3c$,

$-4a+5b-6c$,

$4a-7b+6c$.

Answer 1

Test for collinearity is that thier cross product should be zero.

$3a-4b+3c$

$-4a+5b-6c$

$4a-7b+6c$

$\left|\begin{array}{ccc}3& -4& 3\\ -4& 5& -6\\ 4& -7& 6\end{array}\right|$

$=3\times (5\times 6-(-7)\times (-6\left)\right)-(-4)(-4\times 6-4\times 6)+3(-4\times -7-5\times 4)=-36+0+24=-12$

They are not collinear as the cross product is non-zero.