Question

Test the co-linearity of the set of points with the following position vectors: If they are co-linear then write 1 otherwise write 0.

$5a+4b+2c,6a+2b-c,7a+b-c.$

Answer 1

Considering $a,b,c$ as unit vectors.

Therefore, for the vectors to be collinear, each pair of vectors from the above set of two vectors should have their vector product as 0.

Therefore,

$(5a+4b+2c)\times (6a+2b-c)$

$=-8a+17b-14c$

$\ne 0$

Since $5a+4b+2c$ and $6a+2b-c$ are non collinear.

Hence the above set of point all together are non-collinear.

Hence the answer is 0.