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

Find the equation of the line passing through the point hat i+ hat j- hat k and perpendicular to the lines vec r= hat i+lambda(2 hat i+ hat j-3 hat k)a n d vec r=(2 hat i+ hat j- hat k)dot

Find the equation of the line passing through the point hat i+ hat j- hat k and perpendicular to the lines vec r= hat i+lambda(2 hat i+ hat j-3 hat k)a n d vec r=(2 hat i+ hat j- hat k)dot

Find the vector equation of the plane passing through three points with position vectors hat i+hat j-2hat k,hat i-hat j+hat k and hat i+2hat j+hat k .Also find the coordinates of the point of intersection of this plane and the line vec r=3hat i-hat j-hat k+lambda(2hat i-2hat j+hat k)

Find the vector equation of the plane passing through three points with position vectors hat i+hat j-2hat k2hat i-hat j+hat k and hat i+2hat j+hat k Also find the coordinates of the point of intersection of this plane and the line vec r=3hat i-hat j-hat k+lambda(2hat i-2hat j+hat k)

Find the vector and cartesian equation of a plane containing the two lines vec r=(2hat i+hat j-3hat k)+lambda(hat i+2hat j+5hat k) and vec r=(3hat i+3hat j+2hat k)+mu(3hat i-2hat j+5hat k) Also,show that the line vec r=(2hat i+5hat j+2hat k)+P(3hat i-2hat j+5hat k) lies in the plane.

Find the distance of the point (-1,-5,-10) from the point of intersection of line vec r=2 hat i- hat j+2 hat k+lambda(3 hat i+4 hat j+2 hat k) and the plane vec r ( hat i- hat j+ hat k)=5.

Find the distance of the point (-1,\ -5,\ -10) , from the point of intersection of the line vec r=(2 hat i- hat j+2k)+lambda\ (3 hat i+4 hat j+2 hat k) and the plane vec rdot( hat i- hat j+ hat k)=5