Show that the plane whose vector equation is ` vec rdot( hat i+2 hat j= hat k)=3` contains the line whose vector equation is ` vec rdot( 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.

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

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

Find the Cartesian form of equation of a plane whose vector equation is : vec rdot((12 hat i-3 hat j+4 hat k)+5=0

Find the distance of the point with position vector -hat i-5 hat j-10 hat k from the point of intersection of the line vec r=(2 hat i- hat j+2 hat k)+lambda(3 hat i+4 hat j+12 hat k) with the plane vec rdot(( hat i- hat j+ hat k)=5.

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

Write the plane vec rdot((2 hat i+3 hat j-6 hat k)=14 in normal form.