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+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 vec r=( hat i+ hat j)+lambda(2 hat i+ hat j+4 hat k)dot ​

Prove that the plane 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

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

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

Find the shortest distance between the lines whose vector equations are: vec r=2 hat i- hat j- hat k+lambda(2 hat i-5 hat j+2 hat k)a n d\ , vec r= hat i+2 hat j+ hat k+ mu( hat i- hat j+ hat k)dot

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.

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 .

Find the shortest distance between the following pairs of line whose vector equation are: vec r=( hat i+2 hat j+3 hat k+lambda(2 hat i+3 hat j+4 hat k)a n d\ vec r=(2 hat i+4 hat j+5 hat k)+mu(3 hat i+4 hat j+5 hat k)