[" 48.A point on the line "],[qquad bar(r)=(1-t)(2bar(i)+3bar(j)+4bar(k))+t(3bar(i)-2bar(j)+2bar(k))^(6)]

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

Compute 2 bar(j) xx (3bar(i) - 4bar(k)) + (bar(i)+2bar(j)) xx bar(k) .

Find the shortest distance between the skew lines . bar(r)=(6bar(i)+2bar(j)+2bar(k))+t(bar(i)-2bar(j)+2bar(k))andbar(r)=(-4bar(i)-bar(k))+s(3bar(i)-2bar(j)-2bar(k))

bar(r)=2bar(i)+3bar(j)-6bar(k)" then find "abs(bar(r)) .

The vectors 2bar(i)-3bar(j)+bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+bar(j)-2bar(k)

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

Find the vector equation of the line passing through the points 2bar(i)+3bar(j)+4bar(k), 3bar(i)-2bar(j)+2bar(k) .

If the position vectors of the points A,B,C are -2bar(i)+bar(j)-bar(k), -4bar(i)+2bar(j)+2bar(k), 6bar(i)-3bar(j)-13bar(k) respectively and bar(AB) = lambda bar(AC) then find the value of lambda .