Question

Show that the vectors $2\hat i -3\hat j+4\hat k$ and $-4\hat i +6\hat j-8\hat k$ are collinear.

Answer 1

As we know that...

Two Vectors are collinear only if one is multiple of other

here,let

$\vec a=2\hat i -3\hat j+4\hat k$ and $\vec b=-4\hat i +6\hat j-8\hat k$

if we take -2 common from vector b it becomes multiple of vector a,

$\vec b=-2(2\hat i +3\hat j+4\hat k\\\\\vec b=-2\vec a$

Hence both vector a and b are collinear.