A line passes through the point with position vector `2 hat i-3 hat j+4 hat k` and is in the direction of `3 hat i+4 hat j-5 hat kdot` Find the equations of the line in vector and Cartesian forms.

A line passes through the point with position vector 2 hat i-3 hat j+4 hat k and is in the direction of 3 hat i+4 hat j-5 hat kdot Find equations of the line in vector and Cartesian form.

A line passes through the point with position vector 2hat(i)-3hat(j)+4hat(k) and is in the diretion of 3hat(i)+4hat(j)-5hat(k) . Find the equation of the line is vector and cartesian forms.

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

Find the vector equations of the line passing through the point with position vector (2hat(i) +hat(j) -5hat(k)) and parallel to the vector (hat(i) +3hat(j) -hat(k)) .Deduce the Cartesian equations of the line .

A line passes through the point (2,1,-3) and is parallel to the vector (hat(i) -2hat(j) +2hat(k)) . Find the equations of the line in vector and Cartesian forms .

Find the image of the point having position vector hat i+3hat j+4hat k in the planer.vec r*(2hat i-hat j+hat k)+3=0

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

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)

A line passes through the point (3,4,5) and is parallel to the vector (2hat(i) +2hat(j) -3hat(k)) . Find the equations of the line in the vector as well as Cartesian forms.