Show that the plane whose vector equation is ` vec rdot( hat i+2 hat j- hat k)=1.` and the line whose vector equation is ` vec r=(- hat i+ hat j+ hat k)+lambda(2 hat i+ hat j+4 hat k)` are parallel. Also, find the distance between them.

Show that the plane whose vector equation is vec r*(hat i+2hat j-hat k)=1. and the line line whose vector equation is vec r=(-hat i+hat j+hat k)+lambda(2hat i+hat j+4hat k) are parallel.Also,find the distance between them.

Show that the plane whose vector equation is vec r*( hat i+2 hat j= hat k)=3 contains the line whose vector equation is vec r*( hat i+ hat j)+lambda(2 hat i+ hat j+4 hat k)dot

Show that the plane whose vector equation is vec r*(hat i+2hat j=hat k)=3 contains the line whose vector equation is vec r*(hat i+hat j)+lambda(2hat i+hat j+4hat k)

Show that the plane whose vector equation is vec r . (hat i +2 hat j −hat k ) =3 contains the line vec r=( hat i+ hat j)+lambda(2 hat i+ hat j+4 hat k)dot ​

Show that the line whose vector equation is vec rdot(2 hat i+5 hat j-7 hat k)+lambda( hat i+3 hat j+4 hat k) is parallel to the plane whose vector equation is vec rdot( hat i+ hat j- hat k)=7 . Also find the distance between them.

Show that the line whose vector equation is vec r=(2 hat i-2 hat j+3)+lambda( hat i- hat j+4 hat k) is parallel to the plane whose vector equation vec r( hat i+5 hat j+ hat k)=5 . Also, find the distance between them.

Show that the lines whose vector equation is vec(r) = (hat(i) + hat(j) ) + lambda (2 hat(i) + hat(j) + 4 hat(k)) is parallel to the plane whose vector equation is vec(r). (hat(i) + 2 hat(j) - hat(k) ) = 3 , and find the distance between them. Also, state whether the line lies in the plane.

Show that the line whose vector equation is vec r*(2hat i+5hat j-7hat k)+lambda(hat i+3hat j+4hat k) is parallel to the plane whose vector equation is vec r*(hat i+hat j-hat k)=7. Also find the distance between them.

Find angle theta between the vectors vec a = hat i + hat j - hat k and vec b = hat i - hat j + hat k .

show that the line whose vectors equation is vec r=(2hat i-2hat j+3hat k)+lambda(hat i-hat j+4hat k) is parallel to the plane whose vectors equation is vec r*(hat i+5hat j+hat k)=5. Find also the distance between them.