[" Find the Tmage of point "(1,2,3)],[" in the line "],[qquad vec r=(61+7hat jmath+7hat k)+lambda(31+2hat jmath-2hat k)]

The image of the point (1,2,3) about the line vec r=(2hat i+3hat j-hat k)+lambda(hat i2hat j+2hat k) is

Find the distance of the point (33,3) from the plane vec r*(5hat i+2hat j-7hat k)+9=0

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

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

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 angle between the lines vec r=2hat i-5hat j+hat k+lambda(3hat i+2hat j+6hat k) and vec r=7hat i-6hat k+mu(hat i+2hat j+2hat k)

Find |vec a xxvec b|, if vec a=hat i-7hat j+7hat k and vec b=3hat i-2hat j+2hat k