Show that the vectors `hati -2 hatj+3hatk , -2hati+3hatj-4hatk and hati -3hatj +5hatk` are coplanar.

Answer

`a to q ; b to s ; c to p ; d to r`

Explanation

a. `|veca + vecb|= |veca + 2vecb|`
`a^(2)=b^(2)+ 2 veca. Vecb= a^(2)+4b^(2)+4 veca.vecb`
`or 2veca.vecb= -3b^(2)lt 0`
Hence, angle between `veca and vecb` is obtruse.
b. `|veca +vecb|= |veca-2vecb|`
`or a^(2)+b^(2)+2veca.vecb=a^(2)+4b^(2)-4 veca .vecb`
` or 6 veca.vecb = 3b^(2)`
Hence, angle between `veca and vecb` is acute.
c. `|veca + vecb|= |veca - vecb|`
` Rightarrow veca. vecb`
Hence, `veca` is perpendicular to ` vecb`
d. `vecc xx (veca xx vecb) ` lies in the plane of vectors
`veca and vecb`
A vector perpendicular to this plane is parallel to
` veca xx vecb`
Hecne, angle is `0^(@)`