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Show that the vectors are coplanar ha...

Show that the vectors are coplanar
`hat(i)-2hat(j)+3hat(k),-2hat(i)+3hat(j)-4hat(k),-hat(j)+2hat(k)`

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Show that the vectors are coplanar 2hat(i)+3hat(j)+hat(k),hat(i)-hat(j),7hat(i)+3hat(j)+2 hat(k)

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Let alpha in R and the three vectors a=alpha hat(i) + hat(j) +3hat(k) , b=2hat(i) +hat(j) -alpha hat(k) " and " c= alpha hat(i) -2hat(j) +3hat(k) . Then the set S={alpha: a,b " and c are coplanar"}

Show that the lines vec(r)=(6hat(i)+hat(j)+2hat(k))+s(hat(i)+2hat(j)-3hat(k)),andvec(r)=(3hat(i)+2hat(j)-2hat(k))+t(2hat(i)+4hat(j)-5hat(k)) are skew lines and hence find the shortest distance between them.

Determine whether the three vectors 2hat(i)+3hat(j)+hat(k),hat(i)-2hat(j)+2hat(k)and3hat(i)+hat(j)+3hat(k) are coplanar.

Show that four points whose position vectors are given 6hat(i)-7hat(j) ; 16hat(i)-19hat(i)-4hat(k) ; 3hat(i)-6hat(k) ; 2hat(i)-5hat(j)+10hat(k) are co-planar