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

Find the distance between the planes bar(r) * ( 2 bar(i) - bar(j) + 3 bar(k)) = 4 and bar(r) * ( 6 bar(i) - 3 bar(j) + 9 bar(k)) + 13 = 0

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 point of intersection of the line passing through bar(i)-2bar(j)-bar(k), 2bar(i)+3bar(j)+bar(k) and the plane passing through 2bar(i)+bar(j)-3bar(k), 4bar(i)-bar(j)+2bar(k), 3bar(i)+bar(k)

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

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)| .