Find the equation of the plane through the points (2, 1, -1) and (-1, 3, 4) and perpendicular to the plane `x-2y+4z=1.` Also show that the plain thus obtained contains the line ` vec r=- hat i+3 hat j+4 hat k+lambda(3 hat i-2 hat j-5 hat k)dot`

Find the vector equation of the plane passing through the points (2,1,-1) and (-1,3,4) and perpendicular to the plane x-2y+4z=10. Also show that the plane thus obtained contains the line vec r=-hat i+3hat j+4hat k+lambda(3hat i-2hat j-5hat k)

Find the vector equation of the plane passing through the points (2,\ 1,\ -1)\ a n d\ (-1,\ 3,\ 4) and perpendicular to the plane x\ -\ 2y+4z=10 . Also show that the plane thus obtained contains the line vec r=- hat i+3 hat j+4 hat k+lambda\ (3 hat i-2 hat j-\ 5 hat k)dot

Find the vector equation of the plane passing through the points (3, 4, 2) and (7, 0, 6) and perpendicular to the plane 2x-5y-15=0. Also, show that the plane thus obtained contains the line vec r= hat i+3 hat j-2 hat k+lambda( hat i- hat j+ hat k)dot

Find the vector equation of the plane passing through the points (3, 4, 2) and (7, 0, 6) and perpendicular to the plane 2x-5y-15=0. Also, show that the plane thus obtained contains the line vec r= hat i+3 hat j-2 hat k+lambda( hat i- hat j+ 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 equation of the plane passing through the point (1,1,1) and containing the line vec r=(-3hat i+hat j+5hat k)+lambda(3hat i-hat j5hat k) Also,show that the plane contains the lines vec r=(-hat i+2hat j+5hat k)+lambda(hat i2hat j5hat k)

Find the equation of the plane passing through the point (1,1,1) and containing the line vec r=(-3hat i+hat j+5hat k+)lambda(3hat i-hat j-5hat k) Also,show that the plane contains the lines vec r=(-hat i+2hat j+5hat k)+lambda(hat i-2hat j-5hat k)

Find the vector and Cartesian equations of the line through the point (1, 2, 4) and perpendicular to the two lines vec r=(8 hat i-19 hat j+10 hat k)+lambda(3 hat i-16 hat j+7 hat k) and vec r=(15 hat i+29 hat j+5 hat k)+mu(3 hat i+8 hat j-5 hat k)dot

Find the vector equation of plane passing through the points 2hat i+hat j-hat k and -hat i+3hat j+4hat k and perpendicular to the plane vec r*(hat i-2hat j+4hat k)=10

Find the vector and Cartesian forms of the equation of the plane passing through the point (1,\ 2,\ -4) and parallel to the lines vec r=( hat i+2 hat j-4 hat k)+lambda(2 hat i+3 hat j+6 hat k)a n d\ vec r=( hat i-3 hat j+5 hat k)+mu( hat i+ hat j- hat k)dot Also find the distance of the point (9, -8, -10) from the plane thus obtained.