Show that the line whose vector equation is ` vec r = dot(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 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 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-2hat j+3)+lambda(hat i-hat j+hat 4hat k) is parallel to the plane whose vector equation vec r*(hat i+5hat j+hat k)=5. 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)=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.

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

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 following planes are at right angle: vec rdot((2 hat i- hat j+ hat k)=5\ a n d\ vec rdot((- hat i- hat j+ hat k)=3.

Image of the point P with position vector 7hat i-hat j+2hat k in the line whose vector equation is,vec r=9hat i+5hat j+5hat k+lambda(hat i+3hat j+5hat k) has the position vector

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