Find the vector equation of a line passing through a point with position vector `2 hat i- hat j+ hat k ,` and parallel to the line joining the points `- hat i+4 hat j+ hat ka n d hat i+2 hat j+2 hat kdot` Also, find the Cartesian equivalent of this equation.

Find the vector equation of a line passing through the point with position vector hat i-2 hat j-3 hat k and parallel to the line joining the points with position vectors hat i- hat j+4 hat ka n d2 hat i+ hat j+2 hat kdot Also, find the Cartesian equivalent of this equation.

Find the vector equation of a plane passing through a point having position vector 2 hat i- hat j+ hat k and perpendicular to the vector 4 hat i+2 hat j-3 hat kdot

Find the vector equation of a line which passes through the point with position vector 2 hat i= hat j+4 hat k and is in the direction of hat i+ hat j-2 hat kdot Also, reduce it to Cartesian form.

Find the vector equation of the plane passing through the points having position vectors hat i+ hat j-2 hat k ,2 i - hat j+ hat ka n d hat i+2 hat j+ hat kdot

Find the angle between the vectors hat i-2 hat j+3 hat k and 3 hat i-2 hat j+ hat kdot

Find the equation of plane passing through the point hat i+ hat j+ hat k and parallel to the plane vecr.(2 hat i- hat j+2 hat k)=5.

Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2 hat i- hat j+4 hat k and is in the direction hat i+2 hat j- hat k .

Find the vector equation of the plane passing through the points 3 hat i+4 hat j+2 hat k ,2 hat i-2 hat j- hat ka n d7 hat i+6 hat kdot

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 position vector of the mid-point of the vector joining the points P(2 hat i-3 hat j+4 hat k"")a n d"Q"(4 hat i+ hat j-2 hat k)dot