The vectors `veca=3hati-2hatj+2hatkandvecb=-hati-2hatk` are the adjacent sides of a paralleogram. The angle between its diagonals is……. .

Explanation

We have `veca=3hati-2hatj+2hatkandvecb=-hati-2hatk`
`:.veca+vecb=2hati-2hatjandveca-vecb=4hati-2hatj+4hatk`
Now, let `theta` is the acute angle between the diagonoals `veca+vecbandveca-vecb`.
`:.costheta=((veca+vecb).(veca-vecb))/(|veca+vecb||veca-vecb|)`
`=((2hati-2hatj).(4hati-2hatj+4hatk))/(sqrt(8)sqrt(16+4+16))=(8+4)/(2sqrt(2).6)=(1)/(sqrt2)`
`:.theta=(pi)/(4)" "[:'"cos"(pi)/(4)=(1)/sqrt2]`