[" 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 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 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

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

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

Find anle between planes bar(r ).(2bar(i)-bar(j) + 2 bar(k)) = 3, bar(r ).(3bar(i)+6bar(j) + bar(k)) = 4

If bar(a) = 2bar(i) - bar(j) + bar(k), and bar(b) = bar(i) - 3bar(j) - 5bar(k) then find |bar(a) xx bar(b)| .

Find the value of [bar(i)+bar(j)+bar(k),bar(i)-bar(j),bar(i)+2bar(j)-bar(k)] .

If bar(a) = 2bar(i) - 3bar(j) + bar(k) and bar(b) = bar(i) + 4bar(j) -2bar(k) , then find (bar(a) + bar(b))xx(bar(a)-bar(b))