Question

State True or False.

The following position vectors are collinear.

$a-2b+3c$,

$2a+3b-4c$,

$-7b+10c$.

Answer 1

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

$a-2b+3c$

$2a+3b-4c$

$-7b+10c$

$\left|\begin{array}{ccc}1& -2& 3\\ 2& 3& -4\\ 0& -7& 3\end{array}\right|=1\times (3\times 3-(-7)\times (-4\left)\right)-(-2)(2\times 3-0)+3(2\times -7-0)=-19+12-42=-1$

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