Question

Test for collinearity the sets of points with the following position vectors:If you think they are collinear then write 1 otherwise write 0 ?
$2a+5b-4c$,

$a+4b-3c$,

$4a+7b-6c$.

Answer 1

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

$2a+5b-4c$

$a+4b-3c$

$4a+7b-6c$

$\left|\begin{array}{ccc}2& 5& -4\\ 1& 4& -3\\ 4& 7& -6\end{array}\right|=2\times (4\times -6-(7)\times (-3\left)\right)-\left(5\right)(1\times -6-4\times -3)+(-4)(1\times 7-4\times 4)=-6+90+36=120$

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