" Line "bar(r)=bar(a)+lambdabar(b)" will not meet the plane "bar(r)bar(n)=q" if "

If the line bar(r)=bar(a)+lamdabar(b) is parallel to the plane bar(r).bar(n)=p, then

Find the point of intersection of the line bar(r)=2bar(a)+bar(b)+t(bar(b)-bar(c)) and the plane bar(r)=bar(a)+x(bar(b)+bar(c))+y(bar(a)+2bar(b)-bar(c)) where bar(a), bar(b), bar(c) are non coplanar vectors.

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 skew lines bar(r) = bar(a_(1)) + lamda bar(b_(1)) "and" bar(r) = bar(a_(2)) + mu bar(b_(2)) is

bar( r )xx bar(a)=bar(b)xx bar(a),bar( r )xx bar(b)=bar(a)xx bar(b),bar(a) ne bar(0),bar(b) ne bar(0)bar(a)ne lambda bar(b) . If bar(a).bar(b)=0 then bar( r ) = ………….

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

Let bar(b)=bar(i)-2bar(j)+3bar(k), bar(a)=2bar(i)+3bar(j)-bar(k) and bar(c)=lambdabar(i)+bar(j)+(2lambda-1)bar(k)." If "bar(c) parallel to the plane containing bar(a), bar(b)" then "lambda=