Show that the following vector are co-planar. `hati+2hatj+3hatk, -2hati-4hatj+5hatk, 3hati+6hatj+hatk`

Explanation

Let `veca = hati+2hatj+3hatk`
`vecb = -2hati-4hatj+5hatk`
`vecc = 3hati+6hatj+hatk`

= 1(-4-30)-2(-2-15)+3(-12+12)
= -34+34 = 0
As we know scalar triple product`(vecaxxvecb).vecc = 0`, it follows that the given vectors `veca.vecb.vecc` are coplanar.