The angle between planes `bar(r).(2bar(i)-3bar(j)+4bar(k))+11=0` and `bar(r).(3bar(i)-2bar(j)-3bar(k))+27=0` is

The angle between the planes bar(r)*(2bar(i)-3bar(j)+4bar(k))+11=0 and bar(r).(3bar(i)-2bar(j)-3bar(k))+27=0 is

The angle between the planes bar(r)*(2bar(i)-3bar(j)+4bar(k))+11=0 and "bar(r)*(3bar(i)-2bar(j))=0. is

A point on the line bar(r)=(1-t)(2bar(i)+3bar(j)+4bar(k))+t(3bar(i)-2bar(j)+2bar(k))

The distance between the line bar(r)=2bar(i)-2bar(j)+3bar(k)+lambda((bar(i)-bar(j)+4bar(k)) and the plane bar(r).(bar(i)+5bar(j)+bar(k))=5 is

The lines bar(r)=bar(i)+bar(j)-bar(k)+s(3bar(i)-bar(j)) and bar(r)=4bar(i)-bar(k)+t(2bar(i)+3bar(k))

The vector area of the triangle formed by the points bar(i)+2bar(j)+3bar(k),2bar(i)+3bar(j)+bar(k) and 3bar(i)+bar(j)+2bar(k) is

The shortest distance between the lines bar(r)=3bar(i)+5bar(j)+7bar(k)+lambda(bar(i)+2bar(j)+bar(k)) and bar(r)=-bar(i)-bar(j)+bar(k)+mu(7bar(i)-6bar(j)+bar(k)) is

The vectors bar(i)+4bar(j)+6bar(k),2bar(i)+4bar(j)+3bar(k) and bar(i)+2bar(j)+3bar(k) form

The shortest distance the two lines bar(r)=2bar(i)-bar(j)-bar(k)+lambda(2bar(i)+bar(j)+2bar(k)) and bar(r)=(bar(i)+2bar(j)+bar(k))+mu(bar(i)-bar(j)+bar(k)) is

bar(F),=abar(i)+3bar(j)+6bar(k) and , bar(r),=2bar(i)-6bar(j)-12bar(k) .The value of a for which the toque is 0