Find the vector equation of a lane passing through a point having position vector `2i+3j-4k` and perpendicular to the vector `2i-j+2kdot` Also, reduce it to Cartesian form.

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

p (2,3,-4) ,vecb =2 hati - hatj + 2 hatk Cartesian equation of a plane passing through the point with position vector b and perpendicular to the vector vec(OPQ) being the origin is :

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 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 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 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 sphere with centre having the position vector hat(i)+hat(j)+hat(k) and sqrt(3).

Find the Cartesian equation of the plane passing through point A(1, 2, 3) and which is perpendicular to a vector vecn=2hati-3hatj+4hatk

Find the vector equation of the line passing through the point (1,2,3) and parallel to the vector 3hat(i) + lamda hat(j) - 2hat(k) .

Find the vector and the Cartesian equations of the plane passing through the point (1,2,3) and perpendicular to the line with direction ratio 2,3,-4.