Show that the lines
`vecr=(2hatj-3hatk)+lambda(hati+2hatj+3hatk)` and
`vecr = (2hati+6hatj+3hatk)+mu(2hati+3hatj+4hatk)`
are coplanar. Also the find the equation of the plane passing through these lines.

Explanation

The lines `barr = bara_(1) + lambda barb_(1)` and `barr = bara_(2) + lambdabarb_(2)` are coplanar, if
`bara_(1)*(barb_(1)xxbarb_(2)) =bara_(2)(barb_(1)xxbarb_(2))`
Here, `bara_(1)=2hatj-3hatk," "a_(2)=2hati+5hatj+3hatk,`
`barb_(1)=hati+2hatj+3hatk, " "barb_(2)=2hati+3hatj+4hatk`
`therefore barb_(1)xxbarb_(2)=|{:(hati,,hatj,,hatk),(1,,2,,3),(2,,3,,4):}|`
` = (8-9) hati - (4-6) hatj + (3-4) hatk`
` = -hati + 2hatj - hatk`
`therefore bara_(1)*(barb_(1)xxbarb_(2))=(2hatj-3hatk)*(-hati+2hatj-hatk)`
`=0(-1)+2(2) + (-3)(-1)`
`= 0 + 4 + 3 = 7`
and `bara_(2)*(barb_(1)xxb_(2))=(2hati+6hatj+3hatk)*(-hati+2hatj-hatk)`
` = 2(-1) + 6(2) + 3(-1)`
` = -2 + 12 - 3 = 7`
`therefore bara_(1) ( (barb_(1)l xx barb_(2)) = bara_(2) *(barb_(1) xx barb_(2))`
`therefore` the given lines are coplanar.
The equation of the plane containing these lines is
`barr*(barb_(1)xxbarb_(2))=bara_(1)*(barb_(1)xxbarb_(2))`
i.e., barr * (-hati + 2hatj - hatk) = 7.`