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 rdot( hat i+5 hat j+ hat k)=5` . Also, find the distance between them.

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.

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.

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 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.

Find the Cartesian form of equation of a plane whose vector equation is : vec rdot((- hat i+ hat j+2 hat k)=9

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)

Find the shortest distance between the lines whose vector equations are vec r=(hat i+2hat j+3hat k)+lambda(hat i-3hat j+2hat k) and vec r=4hat i+5hat j+6hat k+mu(2hat i+3hat j+hat k)

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

Vector equation of the plane r=hat i-hat j+lambda(hat i+hat j+hat k)+mu(hat i2hat j+3hat k) in the scalar dot product form is

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is